Where Does iTunes Store Playlists?
Technically, iTunes doesn't physically store playlists onto your computer. The iTunes library will, however, contain related information about the playlists. For example, when you export iTunes library and import later, the playlists will be imported too.
So, what you want to do with the iTunes playlists?
export itunes playlist
You can export your playlists as an TXT, XML, M3U files by selecting the playlists and using the File>Library>Export Playlist.
Option 1: export itunes playlist to M3U
The M3U playlist format was originally implemented in Winamp but it's currently supported by most media players such as Songbird, MediaMonkey, iTunes and etc. As illustrated in the screenshot attached above, please select M3U from the Format drop-down list to export your iTunes playlist to M3U.
Option 2: export itunes playlist to PLS
Unfortunately, you will not be able to export your iTunes playlist to the PLS format. But, you can still import your iTunes library to Songbird and then save your playlists to the PLS format.
Save Smart Playlist Criteria
If you wish to perform a direct backup on your Smart Playlists, then I'm sorry that I have to break it to you that there's no such way around it. Despite that, you can still try to work it round by exporting the library (File-> Library-> Export Library) to the library.xml file and then import it (File-> Library-> Import Playlist). This will duplicate the playlists, including Smart Playlists and their criteria.