GSSMP is a music player designed to work with the GNOME desktop environment. It does not store a database of all your music, but is designed to work with music files organised into directories. It is small, unobtrusive, and tries to do what you would expect, instead of asking you questions.
It remembers which file was playing on exit, and continues that file from the same place when you start again. It remembers tracks you have been listening to recently and displays them in the "Recent" menu.