I'm actually a bit shocked, and saddened, that not a single person called me out on naming Laurel and Hardy the greatest comedy team. I know we have some intelligent people here, and we are on a Three Stooges board, so I'd like to think somebody can think up of a good response.
Well, you were so obviously tanked when you made that pronouncement (all those mile-long ellipses were a dead giveaway), we figured if we let it pass for a day you'd sober up and get your head straight on this issue.
Actually you make a pretty good case for L&H, objectively. I haven't seen enough of their stuff to make a fair comparison (WAY OUT WEST, SONS OF THE DESERT, MUSIC BOX, and a handful of their silents), but you're right about all the qualifications they've got that their competitors don't. BUT, one important checklist item you left off was posthumous reputation. Although all the teams we're talking about here are still enjoyed by people today to some degree or another, I think the Stooges are enjoyed the most by the general public today, on their own merits, as opposed to being watched primarily by fans of old cinema like some of the other teams. Even people who aren't aficionados of classic comedy enjoy the Stooges, seventy years after their heyday. That probably has a lot to do with their relatively "low" brand of comedy, but it still counts for a lot. L&H are iconic today, no doubt, but their shorts are only watched by enthusiasts today, for the most part.
I've got mixed feelings about L&H myself. Oliver Hardy can be hysterical (love the scene in WAY OUT WEST where he's making an awkward pass at the woman in the stagecoach - "Do you believe in Santy Claus? HAHAHAHA!"). But Stan Laurel's simpering simpleton character is just not funny. Credit to him for being the brains behind their material, but I just don't find him very fun to watch. That said, I'll be giving them a proper inspection here soon once I've bumped their DVDs up in my Netflix queue.
My instinct is to go with the Marx Brothers as best comedy team. Between Groucho and Harpo (with Chico as the middle man for them both to spark off of), their act was a beautiful blend of intelligent, surreal verbal humor and physical comedy. Pretty much the full spectrum. And although their movies/plays were mostly written for them, they contributed a lot of their own ideas and personalities to the act (Harpo came up with a lot of his own physical gags, and Groucho's natural wit always through in his performance). Subjectively, I enjoy the Stooges as much as the Marxes, but can't deny that the Brothers were probably a "greater" team. I'd probably rank Monty Python higher than the Stooges too, for some of the same reasons (range of comedy styles, the fact that they wrote all their own stuff, just plain funny, etc.).