I have a domain (for which I pay about $4 per year). I get a number of email addresses (about 100 I think, although I only use about 4 for myself and my family).
Each of these can be set up to forward to a gmail address, which you can read using gmail's normal web interface, POP, IMAP, etc.
You can also set up gmail to "send as" another email address (e.g, recipients don't see @gmail.com in the reply address, they see your email address on the domain that you own) simply by proving that you can send and receive email at that address.
It works very well, is very cheap and allows you to use pretty much whatever email client you want including a nice web-based one.
In terms of providers, there are two in this setup:
- The one through which you actually read your mail. Although I personally use gmail, I believe yahoo also allow you to do the same thing (all they need to do is allow you to send email as a different user than your yahoo email address).
- The one that people send mail to. Pretty much any domain registration company will do. I personally use 1&1 who seem quite good (I have used them without any problems for several years, after transferring from another provider which seemed to take up to a week to forward the email).