Hmm, where to start? Well I guess I should start with my undisputed favorite character: FLANDRE SCARLET
I may be a bit cliche with this, but I don't really care. She's so cute and immensely powerful at the same time, though the Flan I prefer is more misunderstood than psychotic. I like to think of her as more eccentric (almost like me) than sadistically insane. I'd be lying if I said that I wasn't obsessed with her at the moment. The fact that I've collected perhaps 4 times as many Flan pictures as that of any other character is testament to that, I think. I'll admit that her theme isn't my favorite, but it's really catchy and certainly on my list of favorites.
Anyways, enough ranting about Flan. Here are my other favorite characters (in no particular order):
Marisa Kirasame - Her dialogue is hilariously ridiculous. Plus she always came across to me as a good-natured, easy-to-get-along-with regular person (if you can get past her little thieving habit).
Fujiwara no Mokou - Her backstory is interesting and pretty tragic in a way. In addition, she has awesome fire abilities. What more can you ask for? She is also the owner of my (current) top favorite touhou theme.
Remilia Scarlet - Not sure what attracted me to her in particular, but perhaps it has something to do with a certain charisma? I could also be her theme, it's one of my top favorites, so much so that I even learned how to play it on piano (mostly).
Cirno - I love her ability, design, and theme. Most of all though, I love her "never give up" attitude.
Yuyuko Saigyouji - Another character with both an intriguing and tragic backstory. Her carefree and friendly nature coupled with her theme secures her a spot in my list of top favorite characters.
Youmu Konpaku - She is so awesome and badass, I don't even know where to begin. It probably has something to do with the fact that she's one of the only sword-wielding touhou characters. Her theme is also good, underrated even (IMO).
Yukari Yakumo - Gensokyo's resident troll. Another very interesting character with a ridiculously overpowered ability. Yukari's just purely hilarious and awesome.
Sakuya Izayoi - A knife throwing, time-stopping maid, what's not to like? Her theme is one of the most badass theme's I've ever heard, from any game. It's currently my favorite boss theme from any stage 5.
Suwako Moriya - Another carefree, fun-loving, and good-natured character, much like Yuyuko IMO. Also her hat is awesome. Enough said.
Shikieiki Yamaxanadu - Probably the greatest force for justice in Gensokyo and powerful enough to scare even Yukari.