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, .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: