My 'origional' group (since I got back into RPGs a few years back) meets every other Sunday. We used to rotate through systems with one guy DMing, but every once in a while I would run a few adventures (when we played GURPS or WEG d6 SW). When 3rd edition came out we stuck with it (even spawning a 'sister group' on the alternate Sundays for a while).
Once, when my character had been separated from the group (I had to miss a session when I had a meeting for work), I co-DMed an adventure. I played the BBEG and the DM played his minions. It was great, I had him run smack at the parties Cleric (he had killed his sister) and we actually stood and yelled at each other in character (the dogs went crazy). I killed another character twice when I got him separated from the party (he had a magic item that automatically Resurected him). Good times.
My Friday game group used to switch off between D&D and Fudge, then we switched off between D&D and Savage Worlds (50 Fathoms) until a near TPK had us shelve D&D. We finished up 50 Fathoms and are now playtesting an Alice In Wonderland setting for Savage Worlds (we've broken a bunch of stuff already).
So, to answer the questions, we used to run all sorts of different stuff, but now we stick to one main system for each group, not all DMs run different games, and we don't team up all that often (but it was fun when we did).