A 3wt can handle a nice variety of flies. Heck, I can cast size 10 flies with bead-chain eyes on my 2wt at short distance. Any further, and I get the "Clouser Kick".
For lightly weighted wet/streamer/nymph flies in the size 8 and smaller range, I think a 3wt could handle them just fine. For dries, you can probably go up a size or two.
I'm looking at a 4wt to bridge the gap between my 2wt and 6wts.
For what it's worth, TFO makes some dandy 3wt rods from what I've heard.