Personally, I set up mail.app, used it for a few days and went back to Gmail. Other than it notifying you when you get a new message, I didn't really see much of an advantage to it, and Google Notifier does that anyway. One big issue for me is the ability to send mail from different addresses under the same account (admittedly, I could be wrong and mail.app could have that feature, but it didn't seem like it).
Yep, Mail.app can do all that, and lots more. I send everything "from" my Gmail address, for instance, even though Mail sent to Gmail or my school mail in actuality routes over to Mobile Me. Or you can just have one client access multiple accounts directly.
It's way faster for dealing with lots of emails. It allows for offline access, it instantly exposes my 10+ year email archive to spotlight, and doesn't take away my ability to use a web app when I'm on a foreign computer (you can set up Gmail with IMAP, which makes your local client an exact mirror of what's on the web app; I use Mobile Me.) It gives you quicklook. It uses normal system shortcuts. It uses the normal built in Mac text editing field with all its shortcuts, its dictionary, etc.
Basically a native app gives you all of the features of a modern OS, while even the best web app strives for a System 7/Windows 98 level of functionality. Yeah, this is a pet peeve of mine.
