What are the common categories for speedruns?

It varies wildly by game. Each game's speedrunning community will come up with categories that make the most sense for their game and the available glitches.

In general though, the most common categories are going to be any%, 100%, low%, and glitchless, but even these are not always present: for example, Super Mario 64 breaks from this and uses 0 star, 1 star, 16 star, 70 star, and 120 star as its primary categories.

It's also common to use category names that name a particular glitch, such as no wrong warp, no out of bounds, or no arbitrary code execution. And sometimes, you might also see a category called "no major glitches" which means that a handful of particular glitches defined in the rules are banned, but anything else is allowed. Obviously though, these will depend on the game.

For some other games, this framework doesn't work at all like with Old School Runescape, which instead lists very specific goals like "free-to-play ironman champion's guild" as speedrun categories.