To clarify a little (Sorry QM. Never thought I'd be doing this to you), it can also be used more generally, in the sense of 'I have an eclectic musical taste', which I do. I like selected songs from different genres, including drum'n'bass, some heavy metal, lots of pop., the odd bit of Dolly Parton, some classical/gregorian chant, trance, ambient, speed garage, 60s psychedelic, grunge, bit of everything really, but I don't have a type of music that I like in particular. Just, as QM suggests, 'specially chosen' songs.
From dictionary.com:
1) Selecting or employing individual elements from a variety of sources, systems, or styles: an eclectic taste in music; an eclectic approach to managing the economy.
2) Made up of or combining elements from a variety of sources: 'a popular bar patronized by an eclectic collection of artists, writers, secretaries and aging soldiers on reserve duty' (Curtis Wilkie).