Examples are also key to reading mathematics. Whatever you are discussing, you should have a bunch of examples in your head. Eg if you are discussing groups, you need to memorize maybe 10 examples of groups -- trivial, nice groups, some finite symmetric groups, some infinite groups, an asymmetric group or two, and one or two weird examples. Then whenever you listen or read a theorem, think about what that means for your examples, starting with nice cases like R^n and proceeding to ugly cases.
Thanks Prof Ram. I didn't really appreciate memorizing all that stuff at the time, but it's handy now. If anybody needs a dozen examples of any type of group you can think of, grab his old web pages:
http://www.math.wisc.edu/~ram/math541/