First we have Hatoful Boyfriend, a visual novel where you go to a school for pigeons and date them. I'm not making this up. You can get it and its translation
here if you want to play it yourself. Otherwise just read
this thread for entertainment.
Secondly, the full version of
Katawa Shoujo has been released after 5 years of development. This is the game started by 4chan members to make a dating game staring disabled girls. The punchline? Its actually not bad.
If you've never played a VN before: you click a lot, you read a lot, and at certain points you will get to make a choice that will effect the story in some way, then you read some more. Its like a choose your own adventure book with fewer "Goto Pages" and more music and art.