I just found out that Susumu Hirasawa, the music composer of the soundtrack for Paprika, is very kindly allowing people to download two tracks for free on his official site. The tracks are "The Girl in Byakkoya - White Tiger Field" (the song from Paprika's ending credits) and "Runner" (an outtake track not available on the album - I can't remember where in the movie it was used). Hirasawa is also the person responsible for the music of Berserk and Paranoia Agent, so if you liked the music in those shows you'll probably like this music as well.
Here's where I found out about this, and here's where you can get the tracks. Check them out - I hope to eventually get both the movie and the soundtrack. I don't know enough about different styles of music to say exactly what genre these songs belong to. The best I can think of is "pop/techno," but that doesn't feel entirely accurate. If you've got a better way to refer to this music, feel free to let me know. Of the two Paprika songs available for download, "The Girl in Byakkoya - White Tiger Field" is my favorite. It's very sparkly.