Windows:If you're an iTunes user with a bunch of helper programs to show what's playing, grab lyrics, export playlists, organise files and sync with your USB device, you might be able to do it all at once with free utility iTuner.
Many of these have a few other features too, but their feature completeness cannot compare with iTuner, which can maintain your library (by removing dead/duplicate tracks and empty directories), sync your library or playlists with a non-iPod MP3 player, set global hotkeys, export playlists, convert tracks and automatically fetch lyrics all while sitting in your system tray. And of course, it contains all the usual mini-player features — switching tracks, now-playing functionality, rating songs and adjusting volume, except it stays out of your way unless you invoke it with its keyboard shortcut so it doesn't take up any screen real estate (which can be nice, or can be super annoying if you'd prefer it stay on screen since there's no way to do that).
The program itself isn't super lightweight; in fact, it does take up quite a bit of memory — 54MB on my system, which was even a little more than iTunes itself was taking up. If all you need is a mini-player replacement, this probably isn't the way to go — but if you already have three other programs to fetch lyrics, export playlists and clean up dead tracks, you may do well to consolidate that all into one program. Even for the services that iTunes already offers (like file conversion), it's a heck of a lot easier to do it through iTuner's menu than navigate through iTunes' preferences, choose a file type, and then go back to the menu to convert it. If you really want to power up your iTunes, iTuner is certainly worth a look.
iTuner is a free download, Windows only.