Recs.
Updated
VLC is probably the most popular media player on the market, and for good reason. It is free, open source and plays pretty much every single media format.
SpecsUpdate
Pros
Pro Plays anything: discs, streams, files
VLC can play not just files, but disc-based media, or even streams. Tools like LiveStreamer can be used to directly play streams from sites like Twitch.tv or Dailymotion directly.
Pro Surprisingly Lightest on Resources
Yes. Lightest. Even better than the ones known to be light. Both when playing music, only a single song or when playing a video. Either in terms of Ram and Cpu. Compared with almost all, including the ones from Windows like mpc-hc .. or light ones from Linux like Alsa Player, Audacious, SmPlayer.
Cons
Con Lacks libraries and advanced music player features
VLC is a media player first and foremost. There is no library management, aside from playlists, usage of tags is very limited, no rating system and VLC is best at playing a file directly from a folder as opposed to helping you manage or find good songs in your music library.