Aluminum, steel and carbon are all alike in that they're not titanium!
Carbon? Ok, no matter what way you try to spin it, Carbon fiber is basically glorified plastic. Shock absorbing? Well, no one rides a carbon fiber touring bike on a cross country trip. The mountain biking community has a saying, "friends don't let friends ride carbon fiber". This is because it's too fragile and can break. It's most popular cycling use is for road bikes. Even titanium bikes however often have carbon fiber forks and seat posts because carbon fiber is easier to work with and can be easily shaped into any form desired, can be both shock absorbing as well as stiff. Some of the BEST road bikes are constructed of carbon fiber, such as the Trek Madone.
Steel. It's real all right. Good choice for touring and mountain bikes because it's solid, sturdy, strong, absorbs shocks well making it far more comfy than aluminum. Some entry level road bikes are made out of steel, but most higher end ones are constructed from carbon fiber or aluminium--and of course--Titanium! The problem with steel is the weight, but bikes made out of "chromoly" steel tend to be lighter weight, while still retaining the other advantages of steel. The shock absorbing qualities of steel also absorbs some of your pedaling power--slowing you down.
Aluminium. Well, yes it's bone jarring, but it's also inexpensive, lightweight and fast! If you're looking for a fast bike at a reasonable cost, aluminum delivers. Aluminum bikes are springy and responsive, and glide right up hills. It's also the most popular material as it can be used for just about any type of bike, from the cheapest, to some of the best road bikes on the market. It has a "finite" life though meaning each time you put stress on it, it will lose strength and eventually fail. If you ride a lot, after 3-5 years you run the risk of it snapping--same applies to carbon fiber bikes.
So that brings us to Titanium, which offers all the advantages of the others, with the only disadvantage in that it is somewhat expensive, but a top quality carbon fiber bike can cost far more. Titanium is strong, sturdy, shock absorbing, light weight, fast and sprite, infinite fatigue life, virtually indestructible, plus, well, the fact is, it just looks so darn good!