This just in. He was 61.
Probably best known for his work with Paul Verhoeven (RoboCop, Starship Troopers) and his Emmy-winning work on Lonesome Dove, I think his greatest achievement remains his wonderful music for Conan the Barbarian. Listen to his music from the film here, here and here. He seems to owe quite a bit to Miklos Rozsa in particular stylistically, but his “old school” style was still very distinctive. He’ll be missed.
Note: since the 3 links are YouTube excerpts from the film, the last of these may not be considered completely SFW.
Didn’t even know he did RoboCop or ST. CtB is one of the most influential soundtracks ever and is probably only behind O Fortuna itself as the most influential opus on fantasy/sci fi soundtracks. (Of course, Basil owes a debt to Orff in more than a superficial sense: he copied the spirit and the execution of the entire “primitive sound” from him IMO.)
I think he also did the music for The Hunt for Red October. The music was quite stirring, in a Soviet martial anthem sort of feeling.
Conan the Barbarian is the best action movie score of all time.
Red Dawn, too.
Jeez…we lose Poledouris, and how many other evil f**ks are still alive? Tell me how that’s right. 
So long, Basil.
He also did the soundtrack for Quigley Down Under, with Tom Selleck.
I checked out his listing on the IMDB. It hasn’t been updated yet to show his death. A busy man he was, doing a lot of work both for film and TV. I’m sorry he’s gone.