PaaS (platform as a service) cloud providers generally limit you to a fixed technology stack. However, OpenShift and Heroku allow third-party extensions, which can be used to support Haskell.
Warning: The cartridges are currently liable to fail on small (free) gears due to cabal-install issue #2396.
The cartridge comes in several flavours, with just the network and text packages or a pre-installed framework:
Frameworks that don't have their own quickstart template use the network template (also included in every cartridge). I'll be happy to include any contributed framework-specific templates - please open an  with a link to your Github repo.
Heroku buildpack for tryhplay, incorporating Haste and HPlayground. Demo at http://tryplayg.herokuapp.com/.
4 See also