An Introduction to Touhou, for Those Who Are Unfortunate Enough to Know Nothing About It

Arguably, one could say that Touhou is an obscure series of Japanese bullet hell games created by a possibly perpetually drunk Japanese man known as ZUN. One could also say that using the word Japanese twice in the same sentence is redundant, but I digress. ZUN is solely responsible for the main games.
Anyway, the reason that the obscurity can be argued is that the fanbase is absolutely huge. To steal a quote from the TV Tropes' Touhou Crowning Music of Awesome page (click it, I dare you), most of the songs from the Touhou games have anywhere between sixty and two hundred covers.
There is a torrent that features 1.2TB worth of Touhou songs.
Then there's all the fanart, animations, music videos, toys, so on, so forth. Consider it rule 9 of the internet: if it exists, Touhou has done a cross over with it.

See?

 

There's thousands of pieces of fanart. Now whereas ZUN is able to create the games on his own, and compose loads of wonderful music, there is one area that he doesn't really excel in. His art isn't exactly the greatest. Fortunately, this has allowed artists from all walks of life to interpret Touhou in their own style. I would post some of the fanart up here, but there would be far too much good stuff to post. Go search for it on your own, and keep safesearch on... unless you want to find the more questionable pictures, whatever.
Currently, there are thirteen games in the main series. Following is a list of the games, including the official spin offs:

• Touhou 01: Highly Responsive to Prayers
• Touhou 02: Story of Eastern Wonderland
• Touhou 03: Phantasmagoria of Dim.Dream
• Touhou 04: Lotus Land Story
• Touhou 05: Mystic Square

Those five games were released for the PC-98, a Japanese computer from what I can tell. The next ones were developed for Windows, which I am sure you are familiar with.

• Touhou 06: Embodiment of Scarlet Devil
• Touhou 07: Perfect Cherry Blossom
• Touhou 07.5: Immaterial and Missing Power
• Touhou 08: Imperishable Night
• Touhou 09: Phantasmagoria of Flower View
• Touhou 09.5: Shoot the Bullet
• Touhou 10: Mountain Faith
• Touhou 10.5: Scarlet Weather Rhapsody
• Touhou 11: Subterranean Animism
• Touhou 12: Undefined Fantastic Object
• Touhou 12.3: Touhou Hisoutensoku
• Touhou 12.5: Double Spoiler
• Touhou 12.8: Fairy Wars
• Touhou 13: Ten Desires
• Touhou 13.5: Hopeless Masquerade

Immaterial and Missing Power, Scarlet Weather Rhapsody and Hopeless Masquerade are fighting games. Touhou Hisoutensoku is basically an expansion pack for Scarlet Weather Rhapsody.
Currently, Hopeless Masquerade has only been available as a demo, with the full game being released some time this year.
Shoot the Bullet and Double Spoiler combine bullet hell with photography, and Fairy Wars has you freezing bullets.

There are books and manga, with the story written by ZUN and artwork done by people who can actually draw.

There are loads and loads of characters, hence the large volumes of fanart. Since I've rambled on for a fair bit, I will be introducing characters in no particular order in other posts.