What http status code is supposed to be used to tell the client the session has timed out?

Best I can suggest is a HTTP 401 status code with a WWW-Authenticate header.

The problem with 403 requests is the the RFC 2616 states "Authorization will not help and the request SHOULD NOT be repeated." (i.e. doesn't matter if you are authenticated or not, you are not going to get access to that resource, ever).

The problem with 401 requests is it states they "MUST include a WWW-Authenticate header field". As someone has noted it doesn't appear to be in violation of the spec to use a custom value in a WWW-Authenticate header.

I can't see any reason in RFC 2617 why an HTTP 401 status combined with a custom WWW-Authenticate header like this wouldn't be okay:

WWW-Authenticate: MyAuthScheme realm="http://example.com"

The oAuth spec actually seems to do just this, as they recommend this (though they have to my mind an odd interpretation of the RFC):

WWW-Authenticate: OAuth realm="http://server.example.com/"

This doesn't appear to be specifically SANCTIONED by the RFC, but I can't actually see that it's forbidden by it (it doesn't seem to conflict with any MUST or MUST NOT, SHOULD or SHOULD NOT condition).

I wish there was a more specific HTTP status code for timeouts and for things like CSRF tokens being invalid so this was clearer.

I would recommend an HTTP 401.

Whereas a 403 basically says, "You're not allowed, go away and don't come back", a 401 says, "We don't know if you're allowed or not because you didn't bring your ID. Go get it and try again."

Compare Wikipedia's definitions:

HTTP 403 - The request was a legal request, but the server is refusing to respond to it.

HTTP 401 - Similar to 403 Forbidden, but specifically for use when authentication is possible but has failed or not yet been provided.

What about 419 - it is not standard, but the description on Wikipedia seems to fit:

419 Authentication Timeout

Not a part of the HTTP standard, 419 Authentication Timeout denotes that previously valid authentication has expired. It is used as an alternative to 401 Unauthorized in order to differentiate from otherwise authenticated clients being denied access to specific server resources.