Television crossovers are the most analyzed, but other media have a tendency to take things even farther.
Using the broadest definition of crossover (and still excluding fanfic, obviously), there are surprisingly few separate groups of things that are in crossovers within small groups; depending on your definitions, everything that has a crossover at all can be connected to nearly every other crossover.
Other media can be more complicated about it than television tends to be, so before getting into comic books and video games let’s divide crossovers into categories:
1. Two or more series clearly take place in the same universe, in some cases referencing each other even in between the times the characters meet. Examples: the Marvel and DC comic book universes, the DCAU, the Marvel movie universe, the Buffyverse
2. Two series meet by multiversal travel, meaning they’re clearly not in the same universe but are in the same multiverse. Examples: Marvel/DC crossover comics, Jenny Elf being an Elfquest elf in Xanth, Project X Zone
3. Crossover takes place in a new universe where characters from other series naturally exist together; does not impact the main universe of the series involved. Examples: Super Smash Bros., Super Robot Wars
4. Crossovers with public domain works, which may be canonical in only one direction. Examples: League of Extraordinary Gentlemen, Castlevania, Sherlock Holmes appearing in Ghostbusters
5. Cameos of unclear canon status. Examples: guest characters in Soul Calibur, Link and Samus’s cameos in Super Mario RPG