It really pains me to here so many give a knee-jerk "Gmail is the best answer," as I quite strongly feel that that is no longer the case.
When Gmail first came out, I certainly would have agreed with that statement. When I first received a Gmail invite, I placed "make Gmail address main one" somewhere on my to-do list.
Since then, however, Yahoo has mostly-replaced Yahoo! Mail with Yahoo! Mail Beta, which I strongly feel is far superior to Gmail (and far, far, far superior to the Yahoo! Mail Classic). Its main advantage (but definitely not its only) is its GUI, which contains its own tabbing system, the ability to read an e-mail in an iframe merely by selecting it in the inbox, the ability to move between folders via drag-and-drop, and much more.
Last time I tried the Yahoo! Mail Beta, there was no fallback to basic HTML; since I tend to find myself in links quite frequently, that matters. In contrast, Gmail's Basic HTML mode seems to be better every time I try it... that's decisive for me.
Relatedly, but off topic: It still appals me how many sites don't gracefully degrade back to vanilla HTML. Or even check, for heaven's sake, merrily making all of their links Javascript-only. Not nearly as many as assume that you can't possibly be using your own fonts or setting minimum point sizes, admittedly (my eyesight isn't what it used to be, and it never used to be up to much) but even so... I keep hoping that someday a revision of HTML will come out that banishes the javascript: protocol from links altogether.
Yahoo! Mail is both slower and uglier than Gmail. It also forces you to a nasty ad page when you login. Other than that, not bad. I say this having both open on other firefox tabs.
Gmail is my choice only because it is relatively ad-free. Lack of folders, down-my-throat "conversations" instead of individual messages and pathetic editor are a pain in the back. Gmail sucks when you're managing 4-5 simultaneous email threads daily with various random incoming messages.
I use 3 different computers running two OS'es - that is the only reason I use web-based mail. Back in the day when everything was on my laptop, I liked "TheBat!" and ThunderBird.
I don't understand the lack of folders complaint. Labels achieve the same thing, and more flexibly, even, since the same message can show up in various places, and its read status is what it should be.
I use evolution for work email and use its "vfolders" extensively. They have a different name, and they predate "tagging", but they're really the same thing, and difficult to live without.
In gmail, I would prefer proper threads instead of "conversations", but in practice the difference is minimal.
The crappy editor is its biggest problem, but even that can be worked around.
1) Register domain
2) Register Google Apps
3) Shift DNS entries
4) Yeah! 100 x 2GB email accounts, for free, with integrated XMPP! And an incredibly simple administrative interface.
I get frustrated from time to time with the thread-centric organization (especially with long branching threads). Nonetheless, it's my primary mail client.