So stop your cheap comment, 'Cause we know what we feel...
A review of the RPGGeek database shows that items tagged with Multiverse fall just short of 500. You'd think that putting everything into one game would be a whole lot more popular than that. But... it seems like perhaps gamers like to keep their games to a single genre.
Some of the major multiverse style games published include Doctor Who Roleplaying Game and the closely-named Doctor Who Role Playing Game, both obviously derived from the same media franchise. Also, Lords of Gossamer & Shadow, Aether, Torg (and Torg Eternity), Untold, Beyond the Ӕther, Breachworld, Rifts, Chaos Realms, Fringeworthy (3rd Edition), and Jumpers are heavily invested in multiverse style gaming. As are Immortal: The Invisible War (1st Edition), Nexus D20, Nexus the Infinite City, The Order of the Link, Rifts Chaos Earth, TIME LORD, and of course The World of Synnibarr.
Elric!, Elric of Melniboné (1st & 2nd editions), and Stormbringer (5th Edition) are often considered multiverse centered. The Strange also seems to fit the bill. GURPS (3rd Edition) - really any version - supports the style. There are extensive adaptations of Savage Worlds to allow multiverse play. The whole Spelljammer setting of Advanced Dungeons & Dragons (2nd Edition) was sort of orcs in space. Lots of folks think that Empire of the Petal Throne qualifies. And if you want to include the oddball one-off adaptation or fan-made stuff then pretty much any major game will have some type of multiverse component. Even the venerable Dungeon Masters Guide (AD&D 1e) has an appendix to allow D&D players to wander over to Boot Hill (1st Edition) or Gamma World (1st Edition).
But probably the most thoroughly steeped multiverse game is the aptly-named Multiverser - based on the (commonly promoted) concept that you could have one character play in
any every genre. In order to do that, the game had a "universal" engine that claimed to handle everything from dagger-vs-claw to plasma-vs-laser and everything from chainmail-and-shield to powered-up-mecha. Several major systems also have attempted this, occasionally even with some measure of success.
There's also a healthy niche of old school gonzo players. This goes back to the roots of the hobby where dungeons occasionally led out into space, other planets, or even into crashed space ships (think S3: Expedition to the Barrier Peaks). For fantasy purists, these excursions were often distasteful and caused lingering campaign problems (that fighter with a laser pistol...). Others found the whole mélange delightful, even if the mixup broke the rules. One of the more amusing venues of gonzo gaming these days is Crawling Under A Broken Moon. This periodical offers a whole slug of gonzo crazy in every issue. Some of it so gonzo and so crazy that probably it's too much even for average gonzo crazy players. If you haven't enjoyed issues of this gem, I recommend it.
Another really well-known but never played crossover game is the infamous HYBRID. This... uh... thing... started off as a hybrid of HERO System 1-3 and Marvel Super Heroes. But it didn't end there, eventually turning into a hybrid of pretty much everything, except for logic. It's risible that everybody has heard of the game but nobody has ever played it (probably because it's unplayable). Another "gem" in the group is The World of Synnibarr. It's been through a couple different editions, but the 1st edition remains the best known. Like HYBRID, it's known for being one of the worst RPGs ever. Unlike HYBRID, it's completely playable. I'm not saying you'd want to, but you could. It's an accessible bad system.