MPlayer is a movie and not a media player, although it can play some audio file formats (they are listed in the sections below). This is not a recommended usage of MPlayer, you better use XMMS.
You may have problems playing certain MP3 files that MPlayer will misdetect as MPEGs and play incorrectly or not at all. This cannot be fixed without dropping support for certain broken MPEG files and thus will remain like this for the foreseeable future. The -demuxer flag described in the man page may help you in these cases.
MPlayer can use cdparanoia to play CDDA (Audio CD). The scope of this section does not contain enumerating cdparanoia's features.
See the man page's -cdda option which can be used to pass options to cdparanoia.
MPlayer can use XMMS input plugins to play many file formats. There are plugins for SNES game tunes, SID tunes (from Commodore 64), many Amiga formats, .xm, .it, VQF, musepack, Bonk, shorten and many others. You can find them at the XMMS input plugin page.
For this feature you need to have XMMS and compile MPlayer with ./configure --enable-xmms. If that does not work, you might need to set the XMMS plugin and library path explicitly by way of the --with-xmmsplugindir and --with-xmmslibdir options.