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+1 for fastmail.fm, I've been a customer for some time and like their features. You can point your own domain's mail there, set up fairly comprehensive rules for filtering mail into folders, etc. They have a web interface and it fully supports IMAP so you can point your phone, mail client, etc at it.

FastMail's spam protection is ineffective. I have a secondary account with them, and the amount of spam I receive is unbelievable.

That's funny because I have never gotten a single spam email on my fastmail account ever (and yes I do use it on a regular basis).

RoundCube looks great, their Search features look impressive.

The only free version that I found is available with 25MB. To me this isn't really an alternative to the free gmail version.

EDIT: talking about FastMail