In my order of preference and experience. (note I said preference)
Carbon: I feel this is the ultimate building material. It can be exceptionally stiff or customized in ways that is simply not feasible for a steel bike. Sure, you can mix/match steel tubes, but to get something as precise, one would have to make custom mill runs of tubing. With Carbon, one can simply wrap a tube thicker or reinforce a joint better by adding layers. Cost to build: Carbon really is cheap compared to say, titanium. The money comes in from the experience of wrapping and materials handling.
Steel: Nothing rides like it. It's forgiving, you can dent the heck out of it and it will keep ticking. My next MTB will be steel. (current is aluminum) I'd love to have a Carbon MTB, but I've taken a few spills that would have destroyed the bike. My 36er frame is silly stiff and it's made of steel.
Titanium: It's sexy, expensive and springy. It comes in a close third behind steel due to cost. I'd likely buy steel over TI for this reason; unless I needed better environmental controls. (wet environment/etc)
Aluminum: Super stiff. If you can't afford Carbon and need a stiff/light weight bike; this would be what I'd get. I liked the Trek 1000 tandem we had once I had all the parts built up. It was under #28lbs ready to ride and the frame was actually lighter than my Cyfac Carbon frame by a few grams. Equally as stiff, but the road buzz from the aluminum killed it.