There are multiple bands with that name:

1. Unicorn(ユニコーン) from Japan fronted by Okuda Tamio(奥田民生), active in the 80s and early 90s.

2. UNICORN, the progressive melodic-rock band from Sweden. They have recorded album "Ever Since" in 1993 and Emotional Wasteland in 1995. The singer is Dan Swanö from Edge Of Sanity/Nightingale/etc. Nowadays the band is known as Second Sky, with an album anticipated release in 2008.

3. The Dutch trance-producer Ron Van Den Beuken

4. The Belgian trance-duo Mauro Crisci & Tiziano Crisci

5. The Belgian trance-duo Philip Dirix & Prince Peration

6. Unicorn from Austria, medieval and early Renaissance music ensemble

7. The German (hard)trance and techno producer Sebastian Ostermann

8. The Dutch hardcore/gabber duo Youri Gispen & Milos Gispen

9. The Melodic Power Metal band from Italy. They have recorded one album so far. It's called "The 13th Sign"

10. The Heavy Metal band Germany. They have recorded one EP called "The Legend Returns". This band is split-up.

11. UNICORN from the U.S. plays noise drone electronics. W. T. Nelson formerly of Bastard Noise (risen from the ashes of Man is the Bastard) and Sleestak has released a split CD with noise artist 2673, a split CD with Bastard Noise, and a full-length titled "Playing with Light". Less harsh and more melodic than previous projects.

12. Unicorn from the UK played country-rock, and broke up in 1977.

13. Unicorn from Jamaica, a Dancehall Reggae artist.