Then, you have a lot of apps to choose from. The three most recommended, generic video player apps,
AVPlayerHD, GoodPlayer and It's Playing, unfortunately, don't support playlists. However, they all support folders. Therefore, if you don't plan to put your videos on more than one playlist, they may all be OK for you - just use folders as if they were playlists.
Of course, there are a lot of players that natively support playlists; it's just that I don't recommend them as generic, all-in-one players because, in many respects, they're inferior to the three players recommended above. In the list below, I provide you with a quick evaluation of these app and also point out in which cases (with what kinds of material) you can use them as effectively as the above-mentioned three players.
Note that I've also provided a quick tutorial on adding videos to the playlist in the following list:
yaPlayer (if all you want is playing back mov / mp4 / m4v files and not, say, MKV's with AC3, this may be an excellent choice. See
https://forums.macrumors.com/showthread.php?p=16321816 for more info. Note that playlists are called
Video Groups in the app)
RockPlayer2 (also a sound choice for mov / mp4 / m4v playback but
in no way for MKV's. See
https://forums.macrumors.com/posts/16535148/ for more info.
VM Player HD (has a considerably inferior H.264 decoder than yaPlayer or the three most recommended players. However, its hardware playback is still flawless.)
LuberPlayer (I don't recommend this title at all - see
https://forums.macrumors.com/threads/1496138/ for the why's)
AcePlayer (add movies under Media Explorer > Documents > edit (upper right icon) > select > Third (iTunes) icon; playback (and removing titles from playlists via the Tools icon): Playlist in the main menu)
HD Player Pro (your only choice if you have SSA subtitles; add /edit playlist under Playlists tab; selected playback works)
Oplayer (recommended only for HW-assisted mov / mp4 / m4v playback; last-but-one + icon in every row after creating a playlist in the second item from the top in the top left main menu)
BUZZ Player (not recommended for MKV playback; otherwise, decent; move via Edit > select the item(s) > arrow icon)
etc.
(Note that it's not possible to synch video playlists from the desktop iTunes to iOS, unlike with audio ones. Another long-time problem with iOS.)