GoodReader lets you listen to audio files and watch videos. Only those formats are allowed, that are natively supported by iOS.

You have to make sure that your audio files have one of the following extensions: .aac, .adts, .ac3, .aif, .aiff, .aifc, .caf, .mp3, .m4a, .m4b, .snd, .au, .sd2, wav

You have to make sure that your video files have one of the following extensions: .mov, .mp4, .m4v, .3gp, .mpv

Audio player supports auto-start of next song mode. Next audio file from the same folder starts to play upon finishing the current one. Useful for albums and audio-books. Turn this option on in Audio Playback section of Application Settings. Repeat and shuffle options are supported.

Here's an additional information provided by Apple about supported video formats:

• H.264 Baseline Profile Level 3.0 video, up to 640 x 480 at 30 fps. (The Baseline profile does not support B frames.)
• MPEG-4 Part 2 video (Simple Profile)
• audio part can be either AAC-LC audio at up to 48 kHz or MP3 (MPEG-1 Audio Layer 3) up to 48 kHz, stereo audio