Like:
-The gameplay. This probably mostly goes without saying, but I genuinely enjoy playing Touhou on a level that isn't really present in other video games. There are plenty of games I like, but every time I sit down to play Touhou it's exciting and I have a great time. I'm awful at Touhou, I haven't even beaten every main game on normal, but I get a lot of enjoyment out of it in a very direct way.
-The music. Of course, but yeah, it's great. Love it.
-ZUN's art, especially his black and white art. There are a handful of ZUN portraits that are awful (Satori) but mostly I find them charming. And he's pretty bad at coloring. But mostly I think his art gets a bad rap.
-The manga, be it official or doujin. There's a ton of quality stuff here, so much that it caused me to completely drop out of the American comics scene for a year or two while I caught up. I think I would enjoy the official manga and some of the higher-end doujin stuff even if I didn't play the games, it's fascinating.
-Karaage Tarou. That guy is magical. I have all three books of Myon Myon Typhoon framed above my desk. Did you see the sketches from his sketchbook he posted a while back? I would pay so much money for a sketch of Keine or Nitori.
-Etc. I could go on and fill pages with things I like. Individual characters, the setting, fangames, large parts of the community, the Touhou Figmas, Nikutama Soba, the fighting games, so on, so forth.
Dislike:
-The "loli" stuff. MotK is good about shutting this kind of thing down and I appreciate that. Too many fan communities let it go as a cost of doing business or whatever and I do not approve of that.
-Fanworks set in a high school. A big chunk of Touhou is the setting, why make a doujin where you throw that away for no reason? I guess there's no reason someone couldn't make this interesting, but I've never seen anyone do it.
-Lack of horror comics. This is a weird one because Touhou's tone and horror are borderline incompatible, but horror comics are a big point of interest to me and I think it could be done if it was handled very well. I don't want a lot of this, but I think a few could be a lot of fun if someone very talented worked on them. A few circles have come kind of close, but the tendency of doujin stuff to be character-heavy means that the source of the horror usually ends up being "this character is actually evil" which isn't that interesting or genuine. I want to see Reimu exorcise a scary ghost, and I don't see a reason why that couldn't happen within the framework of Touhou. Also, Gashadokuro please.
To be clear I don't want any of this in any official works, but doujins can afford to explore facets of the central work that wouldn't really work well officially. Forbidden Scrollery is almost set up in such a way that it could be a horror comic, and the tone is slightly weirder and closer to a ghost or monster story with horror elements than usual, but it's still ultimately pretty silly. Which is fair enough, but something like that that's just a few shades scarier would be interesting to see.
Neutral:
-Embodiment Of Scarlet Devil. I think it's the least of the Windows games, or certainly down there, and it doesn't really "feel" like part of the canon to me. I don't hate it, I like some of the cast (Meiling and Patchouli), but some of the cast are among my least favorite characters and the overwhelming popularity is a little grating. Millet Soup's mere existence boosts the cast a little in my estimation. Total headcanon.
-PC98 Touhou. This borders on dislike. I don't like the look or feel of these games anywhere near as much as the later games, although I do think Highly Responsive To Prayers is kind of fascinating in its sheer strangeness. I guess I respect these games for their historical value but I don't want them touching "my" Touhou very much if at all. Maybe if I gave it more of a try I would like it more, but I don't got time for that, I got other Touhou to play.
-ZUN's music CDs. I admit to have not given these a thorough try, but I haven't ever been able to get into them. Without the built-in atmosphere of the games to associate with the music I can't process it as easily, and I found them to be kind of low-energy. I think the story associated with them is very interesting, but the music itself has never clicked with me. Glad they exist, haven't figured out how to properly enjoy them yet.