Here are some examples of tools that can be used to convert your playlists from other services to Spotify.
Converts playlists into Spotify playlists. Supports iTunes, text, and Winamp/media-playlist (.m3u) formatted files as well as converting playlists from Last.fm and YouTube. Winner of a Community Site Award for this category.
Converts playlists into Spotify playlists. Supports iTunes, text, and CSV formatted files.
Converts playlists and albums from iTunes into Spotify. Unify lets you drag and drop tracks into Spotify, so there's no need to manually export iTunes playlists.
Soundiiz converts playlists from one streaming service to another. Connect your accounts from a selection of supported music sites, and then drag your playlists from one site box (e.g. YouTube) to another (e.g. Spotify).