What are roads for, and when to build them?

I've started playing Civ 4 recently; it's a great, complex game, and there's a ton to learn.

One aspect that puzzles me are roads. I read something about needing roads to gain access to resources - but my pasture worked just fine without any road! On the other hand, I did need to build a road for, if I recall correctly, an iron mine to start giving me iron.

What resources require roads, and, outside of the movement bonus, are there other uses for them? For example, is there a trade bonus for connecting cities with a road?