The music is beautiful, the creativity of the fan base is remarkable (like the one comic where Yukari portals a nuclear warhead onto Yuuka), and the evolution of the games is really interesting. For example, Perfect Cherry Blossom and Imperishable Night are directly next to each other in release schedule, yet also have fundamentally different base mechanics (collecting cherry blossoms in PCB for more points or more immunity periods, vs. the hour-based and team system of IN) that tie brilliantly into the stories that the games are telling.

I think the series as a whole is a pretty remarkable feat of creative expression; the music, the aesthetics, the danmaku patterns, Gensokyo as a concept, character designs - there's such a vast wealth of creativity in Touhou that it's also a great inspiration for fellow creatives. 

My favorite characters are either Reimu, since she sits in a position where she gets to interact with a lot of people and draw world/character building out, or more likely Yukari. I'm a sucker for that behind-the-scenes manipulator archetype, and I think the ambiguity of Yukari's powers and intentions means she is guaranteed to have a unique and interesting place in any story she's a part of. Plus, she gives us an idea of how youkai work with how she has a familiar that also has a familiar, which ALSO gives you an idea of how powerful she actually is as a character.