Not sure about web applications, but Pandoc [1], git-annex [2], and xmonad [3] are a few examples of successful, reasonably-sized applications written in Haskell. It's definitely worth browsing through their code if you want some examples of idiomatic Haskell in a practical context.

[1] http://johnmacfarlane.net/pandoc/

[2] http://git-annex.branchable.com/

[3] http://xmonad.org/