UPDATE (21/Dec/2012): it's BACK! See THIS.
I've recommended AVPlayer (HD) in several of my articles as a player with an excellent video decoder and feature set and one of the most recommended, best titles for iPhones and iPads alike.
Unfortunately, it (both the small-screen and the iPad versions) has been recently removed from the AppStore. I've talked to the developer. Currently, it's unknown when AVPlayer(HD) is put back to AppStore - it won't happen in the near future (1-2 weeks), that's for sure.
That is, in the meantime, if you haven't purchased AVPlayer previously and want to purchase a new player now, you'll definitely want to check out the alternatives. If you do know what file formats you want to play back, some of them:
- WMV playback (see THIS): ProPlayer, GoodPlayer and, if you're jailbroken and don't need iPad 3 Retina screen support, XBMC.
- H.264 playback with DSP's (see THIS): It's Playing
(A screenshot showing AVPlayer(HD) belons to the (unfortunately, very small) set of iOS multimedia players capable of hardware accelerating MKV and AVI playback.)
- MKV playback: BUZZ Player (HD) (review; it's currently offered at a discounted intro price of $1 / $2 for small-screen-devices and iPads, respectively, which makes it a very good buy for new customers; note that it won't play MKV files with DTS audio!), It's Playing (note that it stutters a bit more than the other, recommended titles; however, the excellent and absolutely unique DSP's it has may make up for this problem), HD Player Pro (if you don't need TV output - see THIS) and, if you're jailbroken and don't need iPad 3 Retina screen support, XBMC. But, of course, if you have MKV files, you'll always want to remux them to native iOS formats (mp4 / mov / m4v). Under iOS, there is simply no way to play back local MKV's flawlessly, not even on jailbroken devices. Remuxing is best done via Subler - see my dedicated article series ((currently) last part). In THIS MacRumors thread, I also discuss these questions.
- MS-MPEG4 (MP4 ASP) playback: ProPlayer, Oplayer (HD for iPad) by olimsoft, GPlayer by Ginkgo Tech, GoodPlayer by Hustmobile - and XBMC if you're jailbroken (and don't need iPad 3 Retina support). Also see THIS for my list.
- SSA subtitle rendering and playback: HD Player Pro (see THIS) and XBMC.