Pure functional programming might not map very well into the web programming environment. But the main impediment is just the lack of infrastructure (frameworks and APIs). It will be a long time (probably never, honestly) before a functional language has as rich a web programming environment as Java, Python, or Ruby.
That said, there are some options.
- HAppS - a Haskell web application server
- Haskell Server Pages
- Links - a functional web programming language
- mod_caml - an OCaml CGI module for Apache
- Ocsigen/Eliom - an OCaml web server/programming framework
- OPA - a commercial web application framework
- Yesod - a web framework for Haskell
I don't have any experience with any of these. Maybe commenters can weigh in on what's worked well for them.