At some point, people started combining games; most notably, "SMZ3" is a two-game randomizer for Super Metroid and Link to the Past (already two very popular games for randomizers), in which you're playing one SNES cartridge that has both games on it and you can step in specific doors to switch from a spot in one game to a spot in the other game.
Archipelago is an evolution of those multi-game randomizers, which combines the logic from each game to ensure that someone is always able to proceed.
And there are options you can choose to make things simpler; for instance, you can prevent certain key items from being very late in the game. But it's also fun to not do that, and end up (say) having to do half a game without an item you usually get in the first few minutes, working around the lack of that item. (For instance, playing substantial parts of a Zelda game without even a basic sword.)
Some randomizer modes also convert a more linear game into a more open-world game, by making it so you can go anywhere from nearly the beginning, though what you can do in those places will still be limited by the items you have.
Beyond that, personally I'd suggest Super Metroid or any Zelda game.
Here's an example with 114 playthroughs (includes some game spoilers in the latter half): https://youtu.be/YwUIfxF3ujo
It doesn't work as well with linear or mostly linear games.
And as another reply noted, sometimes you get stuck ("BKed"). Sometimes each person has more than one game in the randomizer, so they have a couple of options to play further. Sometimes people go watch someone else play until they're unblocked again.
The organizer can also kick inactive players out and release their checks. You could play solo with one or multiple games.
