I have the Incredible. When someone sends me an email, I get a notification on my phone, and it'll show up when I hit the email icon. If I read an email and delete it from my phone, a day later I can log in to my hotmail from a computer, and the email is still there - it's not deleting it from my account. Conversely, if I am using a computer, and delete an email, it is not removed from the email list on my phone.
Have I got a particular sync setting turned off?
Have I got a particular sync setting turned off?