So I'll say first off, Osu! is in no way some kind of fan-made or company-made Touhou based game. Simply put, it's an international multiplayer PC version game of Elite Beat Agents that is in no way affiliated with the original makers of EBA. For those who don't know EBA is a music video game for the DS where you click notes as you play along with the song (Here's a gameplay video for EBA:
http://www.youtube.com/watch?v=X8ohZevlYzM&feature=related). Osu is a much more improved version (IMO) of EBA that's specifically made for PC (here's a gameplay video for Osu!:
http://www.youtube.com/watch?v=s0LgBUMlvwk)Now this may seem pointless at first because it's a game that doesn't really seem to coincide with Touhou at all. However, Osu! "beatmaps", which are the maps that have all the notes and such, are made by users like you. With this said, Osu! offers a huge variety of songs from all over the world, and a HUGE list of songs are actually Touhou-related. I'm pretty sure "every" theme song from every character in all games excluding PC-98 have already been mapped and made available to the generic public to download.
So basically in short, Osu! is one of those games that has a heavy influence of Touhou, despite it not being intentional really. It's free, it's easy and simple to download, and it's fun if you're into these type of rhythmic games.
Game Link -->
http://osu.ppy.shIf you have questions about the game at all feel free to leave it here or in the Osu! forums. If you wish to discuss it here that's fine too.
EDIT: I forgot to mention I run a Skype call that is, in general, based off Touhou. The reason why I state this is because we occasionally play Osu, with me and a few faithfully playing it. If you wish to join us feel free to PM me your Skype username, and I'll add you. (For those who don't know what Skype is, it's a VoIP program that also has an in-built IM system).