The Touhou Project is a series of independently produced Japanese top-down shooters made by a man referred to as ZUN. Specifically, they're a part of sub-genre called danmaku, often translated as 'curtain-fire' or 'bullet hell'. On Easy mode, the games look like this:
On harder difficulties, they look like this:
The games have simple, largely unimportant plots which mostly act as excuses to throw massive amounts of bullets at the player. Controls are simple, with 'Z' firing the main shot, 'X' bombing (referred to as using a spell card), Shift slowing the player and making their movements more precise, and the arrow keys to move.
At the end of every stage (6 stages and an extra stage per game), a boss shows up and has special attacks called spell cards. If the player defeats the spell card within the time limit without either dying or bombing, they 'capture' that spell card and receive a significant score bonus. When killed, enemies drop power items, which boost the power of the player's shot, and point items, which increase the player's score. Depending on which of the games you're playing, extra lives will be given for various things, from getting certain scores to picking up point items.
This video shows someone who's very good at the game playing the fifth stage on lunatic difficulty in Perfect Cherry Blossom, the seventh Touhou game.
As the video may suggest, the Touhou games have excellent music, which has done a great deal to boost their popularity. To close this post,
this is probably my favourite theme from the entire Touhou series.