But I wouldn't use it with ASP.NET. Learning F# is pretty heady and it would give your average .NET developer fits to learn it. You'd lose an advantage of using the .NET platform then - it's pretty easy to get average developers to be productive in .NET/C#. Forcing developers to learn F# would grind productivity to a halt.
Also, because of the whitespace requirements, F# is lousy in the webforms view engine. (Perhaps a Mako-like templating engine for F# would make sense).
Stick with C# for your web work and your libraries that your web site are using. Life will be easier.
If you really want to delve into F# on the web, these guys did a framework designed to be used with F#: http://www.bistroframework.org/
They also did a .NET port of the django templating engine: http://ndjango.org/