The player I recommend (review; another, MKV-specific one), along with the (currently, not AppStore-based) AVPlayer(HD), the most for non-DTS (that is, mostly, AC-3) MKV's on non-jailbroken devices has been BUZZ Player - it has had one of the best MKV behind-the-curtains demuxing and hardware playback.
Unfortunately, as was easy to predict (article), the latest update entirely removed AC-3 support, practically rendering the player pretty much useless for any (except for AAC-only - see below) kind of MKV playback. Again, as has already been stated, MKV's with DTS - the other most commonly used audio format in MKV's - audio can't be played back by the player, as opposed to ones with (up until 4.0.1) AC-3 or AAC tracks. AAC tracks are used very rarely in current MKV's because of their being non-native DVD / Blu-ray audio formats and comparative inferiority, particularly to DTS. Unfortuntaley, the new, 4.0.2 version refuses to play MKV's with not only DTS, but also AC-3 audio tracks using hardware decoding (it uses software decoding), even if the MKV does have a (still-compatible) AAC audio track.
I've annotated this in the AppStore update notes below (click for a larger version), along with the similar Power/GoodPlayer updates:
The solution? As has been (partly - there, I haven't mentioned all versions of BUZZ Player are incompatible with MKV's with an AC-3 + AAC double audio track) explained HERE, either
1. back up the old (4.0.1) version of BUZZ Player before updating and, then, just overwrite the updated version with the older one or
2. remux your MKV's to have an AAC audio track only. Note that you absolutely must delete the AC-3 audio track from the file (as with DTS) if you do want the player to play it back: if you do leave the original AC-3 track there (along with the converted AAC one), the pre-4.0.2 versions of the player won't open it at all, while the new 4.0.2 will only play back it using software decoding. (An example of such an AC-3 + AAC file is HERE. Feel free to play with it, test it in different players etc.) Purely AAC MKV files will be played back in every version. An example of them is HERE - as with the previous one, feel free to test it. (Finally, should you want to play with a strictly AC-3-only MKV test file with the same footage than the other two, HERE it is.)
3, should you have purchased the 3.x version of BUZZ Player, it won't be updated as the new version is a completely different product (also see THIS article) and the 3.x series will not be updated any more. Fortunately, the 3.x series has equally good MKV playback performance as that of the now-current 4.x series. That is, if you have both (3.x and 4.x) versions, stick with the older, discontinued one for strictly MKV playback, should you want to avoid manual fiddling with overwriting dumbed-down, updated versions of the player with the still AC-3-enabled 4.0.0 or 4.0.1 one (4.0.2 and later versions, as you can also see in the screenshot above, don't support AC-3 any more). As has been explained in my previous BUZZ Player review, the two versions can happily co-exist on the same iDevice so selective playback (you watch MKV's in the old and other stuff in the new version) is certainly possible. (Every cloud has a silver lining - at least there is an advantage of moving to a completely different product as there is, now, point in keeping the two different versions of the player on your iDevice.)
Of course, it's possible the BUZZ Player developers offer AC-3 support in the future in the form of an optional In-App Purchase - nothing is certain, though.
Unfortunately, the "in the new version, the MKV files can only have an AAC track in them" is a very severe restriction - basically, you'll end up having to remux all your MKV's and, what is even worse, also delete the, compared to AAC tracks, vastly superior DTS / AC-3 audio tracks so that the files are played back using hardware and not software decoding. I'll talk to the developers about fixing this major problem - along, of course, with the several-months-long, similar bug with MKV files with DTS tracks. If you can, stick with the old version(s) for AC-3 playback - as explained in Bullet 3 above, even the not-any-longer-updated 3.x series will do fine and, as it won't ever be updated, you can avoid having to manually restore it after an update - as opposed to the now-current new version.
What about the other hardware MKV players?
I've tested some other hardware MKV players, of which two had new versions.
PowerPlayer: As has been emphasized above, it also had to drop AC-3 support in the new (1.7) version. In the latter, MKV's with AC-3 tracks won't be opened at all, even if they also have AAC or DTS audio tracks (that is, ones that are compatible with the player). As opposed to the AAC-only one now compatible with version 1.7, the previous (1.6) version played back all the three test files (AAC-only; AAC + AC-3; AC-3 only - all linked to in Bullet 2 above) using hardware decoding. Nevertheless, it's still a bit stuttering so I still don't recommend it over the smoother BUZZ Player or AVPlayer(HD) for MKV playback. The playback of the DTS-only Monsters (it's HERE, linked from HERE) is plain awful compared to the other hardware players - the current PowerPlayer still can't properly play back MKV's with DTS tracks, it seems.
It's Playing 3.5: it seems to have problems with the three MKV files above - it switches to software decoding with all of them. I'll discuss this issue with the developers and update the article with the news. (The DTS-only Monsters was played back almost (meaning a little stuttering now and then) flawlessly.)
AVPlayer HD: all the three files are played back absolutely flawlessly; so does with the DTS-only Monsters.
1080 MKV Player: the yesterday-released, new (2.02) version is compatible with all the three audio configurations (as was the previous version). I assume the Pro version is also compatible as it has the same update description (iOS 6 + iPhone 5-compliance) as the free (tested) one. The DTS Monsters is played back flawlessly too.
The current versions of the two jailbreak-only players, XBMC and RushPlayer+, both play all the AAC/AC-3 test files flawlessly (and the DTS-only Monsters too). Nevertheless, don't forget that XBMC, as of the current, today's(!) build of 12.0-0~alpha7, still doesn't support the high-resolution screen of the iPad 3 so high-resolution videos, while hardware accelerated, don't look as good as in, say, RushPlayer+.
I haven't tested the AppStore-based (not to be mistaken for the vastly better and just-recommended Cydia-based "+" version!) RushPlayer and EC Player because I don't recommend them for MKV playback and there is no new version of those titles. As soon as new versions of any of these players are released, I post a compatibility report update.
UPDATE (22/Nov/2012): I've published a new set of AAC / AC3 MKV (and M4V) test files and declared the above three test files outdated. Please read THIS.