Well, I'm a member of four different groups, so you get four stories.

I'll put them in chronological order.
#1. I joined my first real gaming group in 1982; that group had been going for 2-3 years at that point, and had originally had its genesis in a sci-fi fan group in Green Bay, WI.
Of the core members of the group at the point at which I joined, 3 others are still involved in it. Over the past 23 years, we've had literally dozens of other players come and go...some have only played for a session or two, some were members for years, and dropped out for a variety of reasons. A lot of the "new" members over the years, especially back in the 80s, were referred to us by the FLGS that was in Green Bay at the time, as we had indicated to the owners of the FLGS that we'd be willing to "take in" players looking for a group.
The group's membership has been the same 7 people for about 5 years now. As we're now physically spread out across several hundred miles, we don't play that often (5-6 times a year), but the original D&D "campaign" is still going, as well as several other RPGs that we play.
#2. I joined another group about 10 years ago; this group had its origin in a weekly game that one of the players had started, using his place of employment (a nature center) as a game venue. Players have come and gone in that group, too....new players tend to be brought in by an existing player. We're currently at 9 players in that group.
#3. This group started as a group of guys who worked at the same ad agency as me, who discovered, in talking over lunch, that they all used to play D&D. The group has mutated considerably over the past few years (almost entirely due to people moving out of town), and is now at 4 players.
#4. After playing my first RPGA games at GenCon in 2001, a friend of mine and I learned that there were several Yahoo Groups dedicated to online RPGA play. We joined these, and started to play online. We found some players that we really got along with well, and those tended to be the ones we chose to play with more often. From that, we've sort of evolved a core group of a dozen or so players who play various RPGA campaigns together. We play mostly online, but get together face-to-face to play once or twice a year, primarily at GenCon Indy.