I agree with Jason and John that two-fly rigs can be very effective, and both describe excellent ways to use them. I use multiple flies almost exclusively.
I do have some problems fishing the common dry-with-dropper rig, though. For me, the nymph rolling over behind the dry often causes the dry to land sideways on the water if my cast is made at any angle other than completely vertical. Since I tend to cast at low arm angles a lot, I don't like to fish the dry-with-dropper much. But there are certain times and situations when I do it, though rarely at full casting distance, with excellent results. When I do this, I'm really using the dry to present the nymph in a particular way (this is not the same as using the dry as an indicator, although it may also serve that purpose). So I'm really nymphing.
Most of the time when I fish a two-fly rig it is when nymphing. I'm either trying to get more information faster or simply giving the fish some menu options, because rarely (if ever) will all the fish in the stream be focused on one particular fly. When I feel the need, as Jason said, or when I'm really desperate, I'll put on a third fly. I usually try to fish flies of different size, color, and pattern together, but I have been known to simultaneously throw multiple flies of the exact same pattern if the action is really specific.
Some rig considerations: Lately I've begun using rigs with the flies much closer together (as near as 8 inches apart), and with split-shot much closer to my flies (sometimes only a few inches away). Doing so gives me better line control, and thus allows me to get multiple entrees onto the dinner plate of a fish in a tight lie. If I fish the flies far apart, it is usually with a specific purpose: I'm either trying to fish them at different depths, in which case they are weighted accordingly, or I am fishing a wide, even run in which my flies will all drift at the same speed regardless of the distance separating them (though, in this second case, I still prefer my flies close together most of the time). Also, when using flies that lend themselves to it, I step down my tippet diameter between flies so that my smallest and last fly is on the lightest tippet, to both present the small fly as deceptively as possible and also to keep from losing my entire rig if I get the last fly hung up.
Just some thoughts.
-Shawn