I did some researching on my own of stair-climbing a few months ago and I found some very interesting things.
This one is personally my favorite, and if the modules were made larger, they could potentially climb much larger stairs:
http://www.youtube.com/watch?v=XzKo6KE2H5A
Even something like this is possible in the FRC:
http://www.youtube.com/watch?v=kVEsOxhubFg
The most interesting thing I found was something like this:
http://www.youtube.com/watch?v=uPvj-2KC9G4
But that would be pretty out of the question for FIRST.
But something like this would be extremely interesting to see:
http://www.youtube.com/watch?v=qyVj4...eature=related
I even did some small mental experiments with the mechanics that go into climbing stairs and came up with some pretty interesting ideas.