The short version: When our heroes crossed the streams in the original movie, straight into Gozer's multidimensional portal... "For a split second, we were connected to every reality at once. Every thought we ever had, the core of our beings... they were seeded into the subconscious of the multiverse. Our concepts, our methods..."
So as it stands now, the various realities are:
- Classic Ghostbusters Universe: The first two movies and 'Ghostbusters: The Video Game' happened here, followed by the various IDW comics. It's roughly about ten years now since the first movie, 1994-ish. A spinoff team, the Chicago Ghostbusters (led by the 'Rookie' of the video game, Bryan Welsh) exists in this universe.
- Real Ghostbusters Universe: A slightly alternate version of the characters and first movie happened here, followed by the cartoon series (So call it late 1980's). Their version of Ghostbusters II / TRG & Slimer doesn't seem to have happened for them yet, at least not relative to the Classic Universe (or is that yet another alternate universe?). A variant of the next universe may yet come to pass here...
- Extreme Ghostbusters Universe: Again, a slightly alternate version of the first movie, followed by a slightly alternate Real Ghostbusters, leads to this late 1990s universe where Egon and Janine mentor a new group of Ghostbusters. One of the team here, Kylie Griffin, exists in the Classic Universe.
- Sanctum of Slime Universe: The first two movies happened here, with the latter leading to the creation of a new team of cadets (in a 2011 video game) unrelated to the other universes. The leader of this team, Alan Crendall, is the nephew of GBII's Janosz Poha.
- Answer the Call Universe: The newest and most distantly related of the Ghostbuster teams, an all-girl group (plus one dumb British guy) in a 2010's NYC where the original team never came to be (and apparently don't exist as individuals either, save in sharing their faces with some other people). One of the team here, Jillian Holtzmann, also exists in the Classic Universe as an Twin Peaks/X-Files kind of FBI agent.
One of the comics hints that both Hulk Hogan's Rock 'n Wrestling (with a GB tribute episode) and Filmation's Ghostbusters (70's live-action/80's animation) exists in the GB multiverse somewhere as well. Even further out in the weeds are various console video game versions, a version from the Japanese anime series Tokyo ESP, and even a universe based on Dan Aykroyd's 1983 first draft of 'Ghost Smashers'.