I'm assuming that what you're actually asking about are the pros and cons of various rim depths, so will answer based on that.
I would highlight Pt 2 of Ken's answer - dealing with crosswinds. The amount of resistance deep-rimmed wheels can offer could quite literally blow you across (off?) the road if you're not careful. Under those circumstances the shallower the rims, the more control you'll have over the bike.
Conversely, when there is no wind to speak of, my own experience (I just bought some 6cm rims not so long ago) is that I feel I'm cutting through the air. (Actually its not just a feeling, my speed increase bears this out.) Beautiful.
I have to say though that if I was looking for an all-purpose set of rims for "general use", I'd go for shallower rims - the all-purpose here being key. On the other hand if I were prepared to chop and change the wheels before every ride (depending on wind conditions), then under the right conditions a nice deep rim will feel amazing.
One other thing worth mentioning - I've found the front rim depth to be more critical than the rear - this is probably obvious when you think about it. I haven't done it yet but I could imagine experimenting with my 6cm rim on the rear, but my 2cm rim on the front.