Plus, I must say that with this soundtrack is so wonderful that I would recommend it even to those who have never seen the movie. It's absolutely great!
The music from Shrek both fit the movie perfectly and enhanced it at every turn. From the quirky music as Shrek and Fiona start to fall in love, to the ethereal "Hallelujah" as they miss each other, to the joyous "I'm a Believer" at the celebratory finale, the music added and added and added to the film, without ever distracting from any other aspect.
As to standing alone, many of the songs in the soundtrack pre-dated the film, in the same or another rendition. However, I think that the film "swallowed" the songs, in that they are not unavoidably linked to it, but not in a way but a positive one.
Want to watch a fun movie? Watch "Shrek". Want to listen to fun music? Listen to this soundtrack.