Mac: You can set up notifications for Gmail in a variety of ways. But if you prefer the web app to a desktop app you can't easily get native notification support. Aura makes that possible.
Once you hook your Gmail account into Aura, you'll get native OS X notifications for all your email or only important messages. Click on the notifications, and you're sent over to the web app. If you prefer to shy away from the bloat of a desktop app for email, Aura's a nice way to still get notifications. You get one email account for free with Aura, but to get more you'll have to shell out $6.49.
Aura - Your Smart Gmail Assistant (free/$6.49) [Mac App Store]