This is not quite as bad a book as I had been led to believe. The prose is often leaden - in particular, the cringe-worthy opening passage which I think should be used as a model of how not to write in classes for impressionable young writers, and the numerous info-dumps idicating that the characters have read all the available scientific literature up to 1994 (which is a shame as most of the book is set in 2011). What appears to be the killer idea of the first half of the book - that science can detect the soul leaving the body at death - is simply forgotten for the last third of the narrative, which plays the rogue-AI's in the net cliche as a murder mystery, leading to an unconvincing resolution. The detective character herself violates standard operating procedure by burbling her theories about the crime to one of the key suspects.
But apart from that, the characters were not too unbelievable and the exploration of the issues of artificial intelligence and the scientific basis of the soul not too undergraduate (with all due respect to my undergraduate readers). And he does predict a future Pope Benedict XVI. (Of course, whether the present Pope will still be there in 2011 is another matter.)
Still, it is pretty surprising that this won the 1995 Nebula Award for Best Novel. I confess I haven't read any of the other nominees, and if this was voted better than them I don't really intend to. (Actually, I may have read Beggars and Choosers by Nancy Kress - I know I read one of the later books in the series, and was seriously unimpressed.) The Hugo for the equivalent year went to Bujold's Mirror Dance, which is the start of the superb four-book climax to the Vorkosigan saga (as continued in Memory, Komarr, and A Civil Campaign).
This is not the worst Nebula-winning novel I have read - that title goes to either The Quantum Rose by Catherine Asaro or The Gods Themselves by Isaac Asimov - but it is certainly in the bottom four. I can't decide if I like it less than Neuromancer, because I can't remember anything about the Gibson book, even though I know I have read it several times.
OK, only Rite of Passage by Alexei Panshin to go...