Just off the top of my head, I can think of a few fandoms that have twins, but this is by no means exclusive: LOTR (Elladan and Elrohir), Boondock Saints (Conner and Murphy), Kim Possible (Jim and Tim), I know that Prince of Tennis has twins in it and I'm sure that there are lots of other fandoms with twins. If I don't know it, that's fine by me!
That's it in the official request, because I want to keep this as broad as possible for anyone looking for a challenge to write for during June, but if you want to write twincest, please put a warning on it. :)
Go forth and fic your best!
EDIT: After getting a few questions on this topic, I'd like to edit and say feel free to write about any sort of twin at all. Including different dimensions, alternate universes colliding, evil clones, etc.