I have dove in threesomes several times and have found them to be much more stressful than buddies. The chances of seperation increase quite a bit as often the divers on the wings will get too far apart, necessitating that the one in the middle keep track of both of them. it is for this reason that DAN discourages it. In a Diveralert magazine article a few months ago they discussed this in detail and their conclusion was that it was "generally" a bad practice. The article favored either buddies or a team of four, basically two buddy teams.
I specifically put "generally" in quotes, because as has been stated by Doc Intrepid and Ric, it can be done well. However, I would stress their point on team work. You have to have three divers who are team oriented, have a shared goal, and understand implicitly what is expected of each of them. In SAR diving, teams of three are the standard, however, they are not all in the water at once. In the military, teams of three are common. I can not speak to cave diving, but will defer to the experience of others on that one.