One thing that I love to do in Haskell, and which Haskell is especially suited to, is writing interpreters and parsers. The other week I wrote a brainfuck interpreter (https://github.com/imeckler/skellfuck) in a couple of hours. Parsec, along with monads and functors, make this kind of thing a real joy to write.
http://learnyousomeerlang.com/
Which is a fantastic book, clearly written as a labor of love.
Erlang doesn't have Haskell's type system and doesn't seem to be of much interest for CS research types, but it's awesome for developing certain kinds of system.
I am curious about Haskell myself, and don't tend to need a lot of excuses to learn a language, but I don't perceive a "sweet spot" for it just yet, as in "I could go build X, and Haskell would be a great fit for it". Given how many smart people use it, I'm sure there are a lot of applications for it, but I also get a feeling that there's not one thing that really stands out.