The new Gmail is here, very slowly rolling out thanks to staged rollouts that may take a few weeks to complete. Thankfully, we already have the APK, and it's only a quick download away. The version number is 4.5-694836, and it's beautiful. Gogogo grab it!
Update: If you don't see the categories, go to the desktop version of Gmail, click the gear icon on the top right, and select Configure Inbox.
Update #2: Swipe down to refresh (see 4th screenshot)!
Update #3: You can finally empty the trash and spam folders with one tap (see 6th screenshot). Hallelujah!
Update #4: Having used the new version for a while on a large device (Note II), I can confirm that the move of the bottom bar with useful buttons like Delete and Mark Unread to the top is terrible for user experience. No, no, no. Just no. We need an option to bring it back to the bottom, and that's a fact.
And here's the tablet UI:
Of course, you can also try your luck using the official Play Store listing and see if the update is available there first. But don't count on it just yet - there are hundreds of millions of Gmail users, and Google's plan is to slowly release the update over several weeks.