Likes:
Well, for starters the games are simple to learn, but are still difficult enough to merit great replay value and are great fun, even if I need to get over my ragequit tendencies.
The whole Gensokyo idea. I just like it. It's a fantasy world that's based on actual myths but has enough personality and quirks to stand on it's own. The rules are flexible to allow for all sorts of storytelling possibilities, but are still well-defined so it doesn't feel like something a third grader crapped out.
The characters are fun and endearing. I like how despite appearing to be classic Moeblobs, everyone's basically a big jerkass to each other and their first impulse upon meeting is to attack/insult/try to eat one another. Also, there's a nice blend between of lighthearted silliness and creepier dark stuff, like Flandre.
The music. Just...the music.
I'm gonna have to hand it to the fanon here. While it does get annoying when some people take it too far and get over-defensive, for the most part it's one of the cooler fanbases I've seen. All the artwork, fanfic/comics, music remixes, bands (damn, Cool&Create put on an awesome show), dances, fan games (I have got to get my hands on Touhou Mother and Touhoumon), fan vids, etc. are just plain awesome. And there is a nice sense of community that I appreciate.
I have to admit, I do like most of the memes, except when they're overused and/or pointless.
The fact that ZUN created this crazy franchise by himself, and that he's perfectly fine with all the fanworks. Also, his constant state of drunkenness is pretty amusing.
Dislikes:
The Yukkuri meme creeps the shit out of me.
Chen's uncanny ability to kill me in random spots every single game. At least have some consistency!
The porn. Dear God, the porn. It is single-handedly responsible for me engaging the safe search whenever I look up fanart.
The fact that the better I do at dodging is inversely proportional to my item collecting abilities.
The effin' Last Word in IN.
The crappy continue system in MoF. No, I don't want to do the whole freaking level over again!
The lack of decent t-shirts. I think I've seen maybe two designs I actually like.
That the Makaize anime stopped at one episode.
The inconsistency of the scoring system. Pick a way and stick with it!
The way it feeds my ragequit tendencies straight from the bottle.