I think you mean, by interactive, something with a user interface like a gui. First, see functional reactive programming.
The only project I used it for that was interactive in that sense was an interactive CLI tool. However Oskar Wikstrom wrote a screen cast editing tool so he could make his Haskell screen casts.
I don't think functional style prohibits interactivity (see: purescript which is strongly influenced by Haskell, we use it for all frontend web work now).
