The best ones and why (There are probably more out there that I've not even thought of, but I've tried alternatives to all of the ones below):
1. ProShot. There's nothing else like it on any other platform, and its a bargain too. With a little knowledge, it turns your already pretty-damn-good phone camera (if you have a higher-end lumia, atleast) into an amazing one via giving you full control over the camera much like you would have with a DSLR camera. Everything from manual focus to shutter speed to timelapse, it's got it all. Constant updates and new features added too.
2. Amazing Weather HD. Best weather app bar none, looks great, great live tile and has all the really useful information without also having a terrible interface.
3. Metrotube. This one is a no brainer really. It's donationware (the trial is the same as the full version), so you don't have to buy it at first if you don't want to.
4. Weave. Best RSS feed reader on any platform IMO. Excellent UI.
5. Photosynth. Create interactive panoramas. How could you not want that?
6. Nokia PlayTo. Stream your phone's media directly to any DNLA-compatable device (smart TV's, your computer, etc).
7. Beem. Excellent app for Di.fm electronic dance music radio, with a huge amount of options for genres. If you are into internet radio of the electronica vareity, that is.
8. Pandora. It's ad free only on Windows Phone 8! What more needs to be said?
Things that still suck:
1. All browsers. Sorry, but there isnt' a single good browser on WP8 yet. UC and SurfCube are the current best, but they still are complete and utter **** compaired to other browsers on other platforms. The reason? Almost every browser out there was built with WP7 compatability in mind, tend to be woefully incompatable with the browser standards on WP8, and as such EVERY SINGLE browser on the device has awful stability, or just awful interfaces. UC has the best UI of any browsers and adds a ton a great functionality/quick access that default IE doesn't have, but its extremely unstable. Surfcube is neat but it's buggy (and doesn't get updated nearly enough), also suffers stability issues, and certain things with the UI suck (i.e. pulling down on the cube requires MUCH MUCH more distance to be covered to get to that side of the cube than just switching tabs). The only browser that isn't an unstable or buggy piece of **** is the default browser... but it's tab system is awful and its extremely light on features. Not to mention the crippling bug with IE (and all browsers) that prevent you from typing in text fields larger than one line large (you can at least get around this bug in UC browser by switching to Speed Mode).