It's funny you should say that, because I've never actually played a Touhou game before. Oh, I've certainly tried at least once, but I've given up on it for a variety of reasons: (1) I'm terrible at shmups and would likely get crushed by a danmaku, and (2) I'm on a Mac and Touhou games refuse to work in a virtualized environment. I do play, enjoy, and occasionally win in Touhou Unreal Mahjong though.
Actually, the reason I appear so familiar with Touhou is because I hang around /jp/ and Nico Nico Douga too much and receive a lot of exposure to the massive amount of fan works, which is something that is of note. If you stop to think about it, it's kind of amazing that a bullet hell game would get such a massive fan community producing all sorts of doujin content (tons, in fact): music, manga, games, and even animations. Touhou's big enough to get its own category on Nico Nico Douga now (along with VOCALOID and iDOLM@STER).
So, Touhou is pretty big, but
what exactly is Touhou?
Touhou is a series of vertical shooters (shoot-em-ups, abbreviated shmups) which are actually a member of the subset of shmups known as danmaku. Danmaku is literally "bullet fire" and the corresponding western term is "bullet hell". Touhou is the creation of a guy called ZUN, who created the games as a response to the dire lack of games featuring shrine maidens. The first five games are for the PC-98, and all subsequent games have been made for Windows. The most recent one is Touhou 12: Undefined Fantastic Object, released at Comiket 76 in August 2009.
In addition to its characters, Touhou is famous for its beautiful, but ridiculous bullet patterns. Essentially, the danmaku subset of shmups is all about an immense number of bullets, often forming an elaborate pattern, and your job is to manoeuvre through them (as opposed to reflex based dodging of a few, fast bullets as in other shmups). Also, ZUN is still almost solely singlehandedly responsible for everything having to do with the Touhou games, from the charmingly bad art to the awesome music and bullet patterns.
So yeah, Touhou is pretty cool. Here, have some videos.
Bad Apple!! PV: This is a PV of a Touhou song featuring some classy silhouettes of Touhou characters. It's currently the most mylisted video on Nico Nico Douga, dethroning longtime champion メルト by supercell.
Here's a clear of Touhou 8: Imperishable Night Extra Stage to show you what Touhou is all about.
Cirno's Perfect Math Class: It turns out there are no buses in Gensokyo.
Marisa Stole the Precious Things: SHANGHAI SHANGHAI SHANGHAI SHANGHAI HOLLAND HOLLAND HOLLAND HOLLAND
Touhou Pianoforte: A 25-minute medley of Touhou music on the piano.
Touhou Pianoforte II: A 23-minute medley of Touhou music on the piano.