I don't know, really. I just find a game that got me interested. I mean, I currently run a 3D platformer game, an extreme sports game, particularly skateboarding, a racing game, and... I don't know how to describe The Runaway Rainbow, my main game.
You gonna need a lot of convincing and luck to got me interested in a game.
Real Time Strategy
Most RTS AI is a pushover, but almost any RTS kind of doubles as a fun puzzle game when speedrunning because often you can bypass base building for half the run and hurl your starting army into their base. Sometimes the lategame levels/missions are still fun too because actually using an economy and A-moving is a break after getting used to the rest of the run.
I like to run rogue like games, or any game where each run would be unique due to RNG, such as card games.
I like 2D platformers and webgames, for pretty much the same reasons that people like hahhah, sandstorm, oreo, and output mentioned. Almost all of the games I run are 2d platformers I find on sites like newgrounds, itch.io, or coolmath. I like doing short speedruns because I like optimizing my times. Longer runs aren't as fun because you can't do harder strategies, and you have to focus much more on consistency than strategies or movement. As a result, finishing a long run is much less satisfying than finishing a short run for me.
