Chrome: Google's browser has a pretty nifty notification system. While Gmail can provide some basic notifications through Chrome, Checker Plus lets you automatically read emails out loud and mark them as read from the notification.
The extension has a host of options, including the ability to read your emails out loud to you using text-to-voice software. You can also customise which action buttons the notification shows, including mark as read, delete, archive, star and reply. The extension can also show you the inbox for every account you're logged into in Chrome, so you don't need to have multiple Gmail tabs open.