There is no "Stop" on iPod. Try this, select a song from the "Songs" menu to play, or the first track of any playlist. This will start a new play count. Once it starts playing, hit the "|<<" button and iPod will stop playing and return to the "Main Menu". This may help you if you want to turn iPopd off and then back on with nothing playing.
Also, if you want to "Stop" in iTunes, just select a different playlist in the source menu while a song is playing and hit the "Play" button and iTunes will stop. Then, naturally, just hit play again to resume music.
HTH:)