In 1900, at the start of the 20th century, motorized land transportation of people was almost entirely by railroad. The U.S. then had an extensive steam railroad network of almost 200,000 miles with about 14,000 miles of electric railways, consisting of both streetcar and light-rail lines.  In and around larger cities, many people rode on electric railways but for long distances they used steam railways (=railroads). Where there were no railways, travel was usually by animal or human power (walking and bicycles).
In spite of the inherent efficiency of the low rolling resistance of the railroad wheel on a rail, the steam engines (locomotives) that powered steam railroads in 1900 were very inefficient. Only a few percent of the heat energy of the fuel (coal or oil) was converted to useful work.  Passenger trains were also quite heavy. Electricity for the electric railways was very inefficiently generated. It then took about 8 times as much fuel to generate a kilowatt-hour of electricity as it does today.  Thus, while it may be a surprise to many, rail transportation in 1900 was relatively energy-inefficient.
Today, most all passenger transportation is by automobile and aircraft. These are now (2000) over 5 times more fuel-efficient than the steam and electric railways were in 1900.  Today we get about 32 passenger-miles per gallon (pmpg) for automobiles (including SUVs). Commercial airlines get the equivalent of perhaps 38 pmpg . Note that 2 persons in a car that gets 20 miles per gallon results in 40 passenger-miles per gallon (40 pmpg). But in 1900, railways only got about the equivalent of a little over 6 pmpg. 
Yet total passenger fuel consumption has increased roughly 40 times since 1900. Other things being equal, the fuel consumption should have gone down by a factor of 5 due to greater efficiency. Why has it increased so much? Simple, we now travel roughly 200 times as much as we did in 1900 (by motorized transportation). This is because population has nearly quadrupled and each person travels about 50 times more miles (4 x 50 = 200). 
In United States for the entire year of 1900, on average, a person only traveled 210 miles by steam railroad [ICC-Graph] and perhaps another 130 miles by electric railways  That sums to 340 miles by rail (nearly a mile per day). Today it's 16,000 miles a year, mostly by automobile and airplane, roughly a 50-fold increase over the 340 miles by rail in 1900.  Why did this happen? It was in part due to the introduction of two new types of transportation: the automobile and the airplane.
In 1900, there were almost no automobiles. But the automobile had already been invented, oil fields had been discovered, and oil refineries built, so the stage was set for the "substitution" of automobile travel for railway travel. Roads were paved and automobiles were mass produced so that by the early 1920's there was more travel by automobile than by railroad. [BusFacts-1935]. From 1900 to 1920, steam railroad travel tripled. [ICC-Graph]. So at first, the automobile was not just a substitute for railroad travel but a complement to it. During the 1920's, automobile travel increased by a factor of 6. Steam railroad travel decreased by about 40% and electric railway travel decreased by about 20%. . Thus automobile travel increased roughly 15 times as fast as the decrease in rail travel. [BusFacts-1935]
As a result of the replacement of each mile of rail travel by 15 miles of auto travel, much more fuel was consumed even though the automobile was then about 3 times more fuel-efficient than the steam railroad  and somewhat more efficient than the electric railway. This is but one example of where the introduction of a more fuel-efficient mode, not only failed to decrease fuel consumption but substantially increased it.
How did the improvement in fuel-efficiency (by a factor of 5) happen in the 20th century? Most of it was due to "replacement" of travel on an inefficient 1900 rail system by more efficient auto travel. But some of it was due to significant improvement of the fuel-efficiency of auto and air transport in the later part of the 20th century. Ironically, during the 20th century, rail fuel efficiency improved much more than auto and air. But when that happened, it was generally too late to be of much benefit since rails had already lost most of their passenger traffic. Declines in energy-efficiency also happened at times, only to be followed by rises later on.
Automobile miles per gallon (mpg) started off high in 1900 (25 mpg ?) since autos were small, had tiny engines and top speeds about the same as a bicycle. But mpg dropped rapidly during the first decade as autos became larger and more powerful. As dirt roads became paved, mpg improved. After 1920, mpg seems to have stayed in the range of 13-15 mpg until federally-mandated fuel economy standards were enacted in the 1970's. As a result, fuel-efficiency increased from 13 mpg to 21 mpg over the next 25 years (after 1970). 
In the 1930's air travel was in it's infancy with only a 0.1% market share in 1935 and trains had an 8% market share (80 times greater). In the mid 1930's railroads started replacing energy hogging steam locomotives with efficient and streamlined diesels while airlines acquired the new Douglas DC 3 aircraft to replace poorly streaming inefficient aircraft such as the Ford Tri-motor. In 1935, airlines only got about 13 passenger-miles per gallon on which was twice as good as steam-powered trains which about 90% of passenger rode on. But the new diesel trains were about 4 times as efficient as flying. Electric trains were only about half as efficient as diesel due to the fact that it took about twice as much fuel to generate a kilowatt-hour of electricity than it does today.
The efficiency of propeller airplane continued to increase until their replacement by inefficient jets starting in the late 1950's, causing fuel-efficiency to nearly drop in half to only 14 passenger-miles per gallon by 1970. Starting in the 1970's aircraft jet engines started to use larger fans which blew air around the sides of the engine (something like the old propellers did, only the fans were hidden from view. This significantly increased engine efficiency. Larger airplanes reduced the surface area per passenger as did having fewer empty seats. The result was that in the final 30 years of the 20th century, airplane passenger-miles/gallon increased nearly 3 fold. 
Since long distance travel by auto gets more mpg than city driving, and often has more people in the auto, the "intercity" auto is typically over 35% more fuel-efficient than the airplane is today. 
Starting in the late 1930's, the steam railroads started to replace their inefficient steam locomotives with much more efficient diesel locomotives. In the 1930's, the steam trains only got about the equivalent of 6 to 7 passenger miles per gallon (pmpg) of gasoline  But the new diesel trains got about 40 pmpg (6 times better). During World War II (1942-1945) with gasoline rationing and many trains with all seats full, diesel trains achieved a whooping 85 pmpg.  Unfortunately, by the time dieselization had been completed in the mid-1950's railroad travel had declined to only a few percent of the intercity travel market. 
Just how fuel-efficient is intercity rail today? As compared to 1900, the higher speeds, air conditioning, and electric heating on Amtrak trains tend to make them less efficient. Due to the increase in the fuel-efficiency of the auto after 1970 intercity rail today is unfortunately not much different than the auto in fuel efficiency. .
This includes streetcars, interurban rail (now called light rail), and subways. They rapidly increased in energy-efficiency after 1900 due to the increasing efficiency of electricity generation. From 1900 to 1920, the energy-efficiency doubled, and it nearly doubled again between 1920 and 1930. After about 1930 their energy efficiency exceeded that of the auto but the pace of improvement tapered off. By 1960, the efficiency of power generation had increased by 85% over 1930  and the energy-efficiency of electric rail transit was over twice that of the auto. ,  Unfortunately, by 1960, almost all of the streetcar and interurban lines (about 99%) had been torn up. [Hilton].
After 1960 there was almost no improvement in electricity generation efficiency.  The new rail transit and light rail in the last quarter of the 20th century must be compared with an auto of increasing fuel efficiency. So today, electric rail transit is only perhaps about 25% more energy efficient than the auto-SUV in urban use. See  and [TEDB]
Buses were not made until 1921. Before then, automobiles and modified trucks were used as buses. These likely had better energy-efficiency than private automobiles since they likely had a higher percentage of their seats full.
The bus is basically the same technology as the auto but uses less fuel per seat due to high pressure tires and less wind resistance (aerodynamic drag). But urban buses waste a lot of energy frequently stopping for passengers and are much less energy-efficient than intercity buses (such as Greyhound).
Today, the urban city buses do little better than the automobile in energy-efficiency, but the intercity buses are the most energy-efficient mode of travel and get over 125 pass-mi/gallon. See  and [TEDB] and . While intercity buses have seemingly somewhat improved in energy-efficiency during the 20th century, urban buses have become significantly worse starting about 1970. Part of the reason may be subsidy, which permits urban buses to continue operating even when they have few passengers. The intercity buses are not subsidized and must maintain high passenger loads (resulting in high energy-efficiency) in order to survive.
During the early 20th century, the dominant mode changed from rail to auto. In the 2nd half of the century, air travel became of major significance. Energy efficiency improved since the new modes were much more energy-efficient than the old rail mode was in 1900. Technological improvements (with setbacks at times) also helped. But ironically, if the auto and airplane hadn't been invented and most all travel was still by rail, fuel efficiency would have likely increased even more, since government might have mandated energy-efficiency standards for rail like they did for autos. And without the convenience of the auto and the high speed of the airplane, there would have been far less travel. Thus far less energy would have been consumed.
So did going from rail to auto and air increase energy-efficiency? Yes and no, depending on how one looks at it. What is clear is that the huge increase in travel caused both by these new modes and also by population growth, resulted in a huge increase in energy consumption.
In the distant past, when land transportation was animal-powered, it was found that an animal could pull a much heavier cart if the wheels were placed on wooden rails. This was the first railroad. Railroad development was of little significance until the practical railroad steam engine was developed in 1825 in England. [TR p.75-6] By 1840, the U.S. had a few thousand miles of steam-powered railroads which exceeded that of the rest of the world combined. By 1860, railroad mileage had increased by ten fold and the railroad become the predominant form of motorized land transportation for both passengers and freight. [TR p.79] Railroad mileage continued to rapidly expand, reaching a maximum of 250,000 miles in the 1920s. In addition there were over 30,000 miles of urban electric railroads (including streetcar lines). 
But the dominance of the railroad was not to endure. Huge amounts of underground oil were discovered in the late 1800's  and this made automobile (and truck) transportation feasible. Steam remained king of motorized transportation for nearly 100 years, not because the automobile (and truck) couldn't be invented but because there was no cheap liquid fuel available to run them on.
So prior to steam power, transportation used renewable energy using sails at sea and plant-eating animals on land. Early railroads burned wood instead of coal, but the rate of depletion of forest trees became unsustainable. So in the mid 19th century, railroads were switching from solar-grown wood to non-renewable coal. See . The "fuel-efficient" railroads were thus starting us down the road to an energy-intensive transportation system dependent on fossil fuels (which in the long run is also unsustainable).
Can we go back to burning wood for land transportation? At the peak of wood-burning trains in about 1865, rail travel was only about 10% of what it was in 1900. Thus, while wood could support motorized travel then, how could it support the travel volume (in passenger-miles) of today which is about 2000 times greater? While we could produce power by burning wood with much greater than the 2.5% efficiency of the railroad locomotives of 1865, by no stretch of the imagination could we accommodate a 2000 fold increase in travel using wood as a fuel. See .
The railroad was invented and became widely used mainly because it took less mechanical energy to move it in an era when the cost of such mechanical energy was high due to inefficient engines. But it's difficult to argue that it saved us energy since before railroads, transportation used wind and animal power.
The automobile was at first much more fuel-efficient than the railroad. Yet owning an auto resulted in so much more travel that it didn't save energy either. The magnitude of the energy consumed by the automobile, dwarfed that formerly consumed by rail travel.
The airplane enabled people to consume the maximum amount of fuel in the least amount of time. Air travel not only consumed more fuel per passenger-mile but the consumption per passenger-hour was many times higher than the auto due to the higher speed.  They enticed people to make very long (and often unnecessary) trips.
Thus it seems that Neither the railroad, nor the auto, nor the airplane saved us energy. Instead, they all enticed us to travel more and thereby consume much more energy.
Some people erroneously think that a major reason for the high fuel consumption today is because we abandoned rail to opt for the auto and airplane. In other words, we are using the wrong modes. But if we continued to travel as much as we do now and did it all by rail, we wouldn't save much energy either, since the energy efficiency of rail isn't much better than the auto. In reality, if rail were the only option for travel today, the volume of travel would sharply decline due to the inconvenience of schedules and access. This would save a lot of energy, not because of rail but because of less travel.
If other things are equal, increasing fuel efficiency obviously saves (conserves) energy. But history shows that the savings due to increased fuel-efficiency can easily be wiped out by increased population and travel. The general concept that increased fuel economy doesn't always save energy due to such other factors is a very old one, first proposed in 1865. 
There are numerous examples of this concept in transportation. One is the paving of dirt roads in the 1910's and 1920's which enabled autos to get more mpg. But a paved road attracts a lot more traffic than a dirt one. Another is the construction of a freeway so that autos will get better mpg than they do in stop-and-go driving on city streets. But the freeways encourage people to live further away from work and otherwise travel more. Building a rail transit system is yet another example. It may remove autos from the highways at first, but later, the resulting lack of congestion on the highways attracts still more drivers. Between 1970 and 2000, auto-SUV fuel economy increased on average at 1.5 % per year. If other things were equal, this would have decreased fuel consumption by 1.5% per year. But instead of a decrease, fuel consumption increased by 1.5% per year (on average) due to increased travel. See TEDB and .
Thus, just increasing energy-efficiency alone may not result in any energy savings. Conserving energy usually also requires measures aimed at decreasing travel such as taxes or rationing. See Travel Less. To do this right is complex since if people travel less, the resulting money saved (or tax revenues) may be spent on using more energy in non-transportation ways.
The crux of the transportation energy problem is that there are just too many people doing too much travel. The development and improvements of the motorized modes of transportation have enticed people into traveling more. The increased travel (and increased population) in the 20th century not only canceled out the 5-fold gain in fuel efficiency but increased fuel consumption for travel 40 times. Thus, in addition to striving to increase fuel efficiency, it's even more important to strive to reduce the need for travel as well as to reduce population.
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