Don't know about best, but www.fastmail.fm/help/overview_features.html is pretty cool. It is what it says, fast. No graphics, clean web interface, runs quick on anything, including crappy old hardware or phones. Opera recently bought them so if you run Opera on your phone it is especially nice. Very reliable, hardly ever down and on the rare occasions it goes down it's usually back up within minutes. You can hook up pretty much any client you like, of course. And they don't read your mail to serve you ads.

I personnaly use Fastmail and I'm very happy with it. As any other serious competitor, it's not free, though, around $50 a year for the best plan (10gB, custom domain and file storage, among other goodies).

I've been playing around with OSX Lion Server installed on my home fios connection on a mac mini server. Apple built a webmail interface that's not as good as gmail, but works if you primarily use a client and just need webmail sometimes.

I'm not ready to switch to it full time, but have been curiously looking around for alternatives to gmail. In general, running an email server yourself is a bit of a pain.

Personally, I use and recommend Gandi (https://www.gandi.net/). If you purchase a domain name from them ($15/year or less), you can use their email with your domain. You can either use a standard mail client with their SMTP and IMAP servers, or you can use their webmail interface (roundcube). Plus, you get an email at your own domain, and you can thus easily switch email providers without changing your email address.

http://www.tuffmail.com/ You pay for mailbox size, with no limit on the number of email aliases or domains you can map to it. They also host Roundcube webmail.

I started out looking for dedicated email services. But in the end I found that regular old shared hosting accounts provide email.

Also, be advised that Iceland has implemented strong privacy policies, and that might be a good jurisdiction to host your email.