MPD is designed around a client/server architecture, where the clients and server (MPD is the server) interact over a network. Thus, running MPD is only half of the equation. To use MPD, you need to install a MPD client (aka MPD interface).
mpc - a solid, lightweight, simple mpd client, written in C.
ncmpc - A curses client written in C.
ncmpcpp - A curses client written in C++ tailored after ncmpc.
netjukebox the flexible media share - netjukebox is a web-based media jukebox for MPD, VideoLAN and Winamp/httpQ.
MPD.FM - A mobile-ready web client focussed on playing internet radio stations
Sonata Client, now ported to Gtk3. At the writing time - more recent, compared to some other gtk clients.
gmpc (Gnome Music Player Client) - A fully featured client.
ario - Another GTK based client.
Cantata - A Qt client.
mpdscribble - Last.fm scrobbler
There are many more clients. Please help and add them to this list.