Android only: Gmail on the web offers a very helpful Priority Inbox, but on Android, you can't get the same kind of only-the-important-stuff filtering. Install Labelert, though, and you can give Priority/Important emails their own LED, ringtone and vibration patterns.
Labelert's a kind of one-use app, but the best kind. It asks you to pick out labels from your various Gmail app accounts, then choose to receive notifications based on new messages in that one particular label. If you pick the "Important" label, those are your Priority Inbox messages, and you can have them blink your LED red and show up in the Notification Bar as distinct from other mail messages.
Labelert is in beta, and some app reviewers have noted some quirky problems on certain hardware. It seemed to work fine on our Nexus One, though. It's a free app, available through the Market or with a QR code scan at the developer's site.