I also would recommend gmail. Though I haven't spent any time with the other big webmail systems. I always got overwhelmed with spam in hotmail, yahoo-mail, etc. With gmail, I rarely have a spam email get past the filters, and it is fast and reliable. I got an invite way back in the beginning, and I cannot recall a single time that I have ever been unable to access it. I have had trouble with the new feature that lets you have gmail check other pop accounts. Emails were showing up days later in gmail than they were getting to my pop client.
When I first started using gmail, I found a little utility that helped me forward every single email from my Outlook mailboxes to my gmail account. I recently got a copy of TheBat! for my various pop accounts, and I set gmail to let me download every single one of my gmail emails through pop. It took a little while, and it downloaded in spurts (I just set TheBat! to check that account every 3 minutes), but eventually I had all 13,632 emails downloaded dating as far back as 1997. What am I going to do with all of those? I don't know, but it was nice to see that gmail and TheBat! could handle it.