The party's over and you want to get rid of that iTunes playlist. Start by clicking it in the Source list and then pressing Backspace (Delete). iTunes presents you with a warning box, double-checking that you really want to vaporize the play-list. (Again, this maneuver just zaps the playlist itself, not all the stored songs you had in it. Those remain available in the main iTunes window.)
If you have your iPod set to autosync, any playlists you delete from iTunes will disappear the next time you plug in and sync your player.
If you manually manage your iPod and all its contents, connect the player and spin open the flippy triangle next to its name in the Source list. That gives you a look at all its libraries and playlists. Click the one you want to dump and hit the Backspace (Delete) key on the keyboard.