The long ARM of Gil Hamilton and its sequel, The Patchwork Girl, by Larry Niven.
Dream Park, by Larry Niven and Steven Barnes (I know there's a sequel to this, but I don't actually own it. Yet.)
The Gumshoe, the Witch and the Virtual Corpse and its sequel, Gumshoe Gorilla, by Keith Hartman.
The 13 Crimes of Science Fiction, edited by Isaac Asmiov, Martin Greenberg, and Charles G. Waugh.
The Caves of Steel and its sequels, The Naked Sun and The Robots of Dawn, by Isaac Asimov. (further sequels are science fiction, but not mysteries)
Dirk Gently's Holistic Detective Agency, by Douglas Adams (just barely qualifies 'cause there's an extraterrestrial involved, otherwise the ghost would plunk it into fantasy; the sequel, The Long Dark Tea-time of the Soul, I consider fantasy, since it deals purely with gods/supernatural)
The Demolished Man, by Alfred Bester.
"Little Fuzzy", "Fuzzy Sapiens", and Fuzzies and Other People, by H. Beam Piper. The first volume is technically more a legal fiction than a mystery, but the trilogy as a whole does contain a couple of crimes and their solutions/judgment all hinge on the legalities of just how intelligence is defined and what constitutes admissible testimony.
EDITED TO ADD: Galaxy Jane, by Ron Goulart. Don't know how I forgot Goulart ... shall have to take a quick look through the rest of his that I have ... some are more spy than mystery, but all are funny. :-)
So, what else is out there that I've missed and need to read?