Webmail as an idea is great, but as of yet there are couple of things that make current implementations bad:
- Slowness. Most of the services are really slow. I once showed my father (who used Iobox's service) what I could do from a shell account. "What? It was already sent?" =)
- Lack of power, or, if the power is there all right, the slowness of the power. Your average E-mail client program has million and one interesting features that take no time to execute, but in webmail you need to wait seconds or even minutes to do anything interesting - as an anti-spammer, I would get easily annoyed if displaying headers would take many seconds. If, of course, it can be displayed at all.
- Insecurity. I prefer to read my mail from a box that I can ssh to; there are some webmail services that offer SSL. But the rest... well, as secure as unencrypted transmission usually is.