Yes, some big-name film composers have done the odd logo. So take a bow:
Danny Elfman (Hollywood Pictures and Regency - this was actually taken from his music for Sommersby),
Dave Grusin (the original Tri-Star logo),
Thomas Newman (Imagine Entertainment),
John Williams (DreamWorks and Amblin Entertainment),
Alan Silvestri (ImageMovers - Robert Zemeckis's company),
and the late Jerry GolRABmith (Carolco, Cinergi, C2 Pictures and the current Universal logo) and Michael Kamen (Silver Pictures, Morgan Creek - taken from Robin Hood: Prince Of Thieves).
Apparently James Horner also did the Lionsgate music.