Basic Email: Yes (though browser load is slow)
Google Docs: Yes (though browser load is slow)
Youtube: Kindof, but I wouldn't suggest it often
Any Actual Games: No, unless you can compile Steam from Source, I don't think it supports ARM. Snake would work fine...
The Raspberry Pi isn't really fit for use as a computer for those used to decent performance, it's good for embedded/dedicated applications or to get low cost computers into cultures that cannot really afford computers.
The idea is to get a start of familiarity and some programming experience, very basic computer functions. But just loading the web browser is fairly slow.