Forgot to mention:

Titanium and high quality steel (Reynolds 853 and similar) are springy and comfortable for long rides, especially on rough surfaces. They are also very durable, and because of the springiness of these metals, the frames can be more readily repaired (a bent tube can often be straightened rather that replaced) and the rear frame width can be "re-set" to a different width, if, heaven-forbid, the bicycle industy decides yet again to increase the width of rear hubs (they have already gone from 120mm to 126mm to 130mm for road bikes just during the past 15 years or so). Titanium needs the least care of the 2 materials, as it doesn't rust, but it is also more expensive. It is a bit lighter than steel also.

Carbon fiber is also very lightweight and excellent at shock absorption, but it is also expensive and occasionally carbon fiber frames have been known to break, though this is more rare these days. Carbon fiber frames cannot be readily repaired (would have to be redone at the factory). Carbon fiber also cannot be reset to a wider width. (My carbon fiber bike is stuck at 126mm (seven speed) and cannot be changed to 8, 9 or 10-speed which requires the new 130mm width.) Hopefully (I've got my fingers crossed) the bike industry will stay at 130mm, but who knows. Sigh.

Aluminum is a very stiff metal and gives a harsher ride, though this can be softened greatly with a carbon fiber fork. (Springs are never made out of aluminum because aluminum gets metal fatigue and breaks when it is flexed much). Aluminum is ideal for sprinters who need maximum rigidity for the greatest burst of speed, but isn't as comfortable for fitness or century riders, especially on rough surfaces. Aluminum also cannot be repaired or reset to a wider width, as it is just too brittle and will break if bent. A bent tube requires replacement at the factory. It is lightweight and inexpensive and it doesn't rust, which makes it one of the most popular frame materials, but I personally would stay away from it due to its harshness.