Google's popular Gmail has already required a security patch that allowed a third party to easily log in and gain full access to one's mail.
I'm amazed at people's willingness to hand over all their private and/or business correspondance to a third party that can do anything it likes with it. Yes, they have a privacy policy, but they also reserve the right to change the privacy policy without your permission.
Gmail, by all accounts, has done a great job with the interface for the software, and in general, email clients desperately need better design in this area. But the risk is just too high. I'm keeping my email on my own machine, under my own control.