iTunes will only let you copy your purchases directly from an iPod to the computer, you'll find details in this article:
Copying iTunes Store purchases from your iPod or iPhone to a computer
For everything else (music from CDs, other downloads and including iTunes purchases) there are a number of third party utilities that you can use to retrieve the music files and playlists from your iPod. I use Senuti but have a look at the web pages and documentation for the others too. You can read reviews and comparisons of some of them here (you'll find that they have varying degrees of functionality and some will transfer movies, videos, photos and games as well):
Wired News - Rescue Your Stranded Tunes
Comparison of iPod managers
A selection of iPod to iTunes utilities:
Senuti Mac Only (iPod Touch & iPhone compatible)
expod Mac Only (iPod Touch & iPhone compatible)
PodView Mac Only
PodWorks Mac Only
TuneAid Mac only (iPhone and iPod Touch compatible)
YamiPod Mac & Windows
iPod Music Liberator Mac & Windows (iPhone and iPod Touch compatible)
iPodRip Mac & Windows (iPhone and iPod Touch compatible)
iPod Music Liberator Mac & Windows (iPhone and iPod Touch compatible)
iGadget Mac & Windows (iPhone and iPod Touch compatible)
Floola Mac & Windows
Music Rescue Mac & Windows (iPhone and iPod Touch compatible)
iRepo Mac & Windows (iPhone and iPod Touch compatible)
iPod Access Mac & Windows (iPhone and iPod Touch compatible)
TouchCopy Mac & Windows (iPhone and iPod Touch compatible)
There's also a manual method of copying songs from your iPod to a Mac or PC. The procedure is a bit involved but if you're interested it's available on page 2 at this link:
Copying Content from your iPod to your Computer - The Definitive Guide