I pay a very small amount to have my own mail server on my own domain. It is unlikely to ever change (great for long-term networking) and I control exactly how crappy or excellent the service is.
Considering how important email is to each of us in our daily lives, even non-hackers, I'm surprised more people don't pay for it.
- You can't. - You can, if you use a native client through IMAP. Both Mail.app in OS X and Thunderbird work very well.
There are some open source projects out there that try to do a good webmail interface. It's been over a year since I last scoped out that scene, but there wasn't much stable, mature stuff back then.
This setup gives me the best web mail client without vendor lock in, I can switch to my own server any time I want and keep all email addresses.