For hardware video playback, mVideoplayer is great. Subtitle and automatic subtitle downloading, gesture support, loads of other features. Is free with ads, I think, but I have those blocked so I can't say for certain. For software video playback... Rockplayer, plays most files perfectly. Costs money though. There's also moboplayer which is free, it's in beta and kinda buggy though, but looks promising and plays most of my normally unsupported files well. Also it's not on the market.
As for music I like doubletwist, it's free and has a nice, clean GUI.