USS Beharry - Named after Lance Corporal Johnson Gideon Beharry VC, youngest winner of the Victoria Cross, and also only one of six people for whom their VC was not posthumous. Named a cruiser after him, and if you look him up, you'll see why.
USS Penrose - My dinky little Nova class science vessel. In keeping with the Scientist/philosopher/scientific phenomenon naming convention, I named it after Sir Roger Penrose, a darn clever physicist, and a guy who describes himself as a "recreational mathematician."
USS Dauntless - My Defiant-class escort. A double name reference (and yes, i know there's a Dauntless in canon somewhere) for both A) The british warship, and more importantly B) The Dauntless, Kimball Kinnison's main ship from the Lensman series.
U.S.S. Nightfall, Galaxy-class
Named for one of Isaac Asimov's most famous works
U.S.S. Apropos of Nix, Excelsior-class
Supposed to be named the Apropos of Nothing, but that was too long. Named after Peter David's character from the book series of the same name. Funny read, the first two. Third book has an unpleasant ending but is otherwise pretty good.
U.S.S. Red Knight, Prometheus-class
Named for a demigod in Faerun (Forgotten Realms D&D setting). That and I liked the chess-like reference for my tactical officer.
You see four ships in my sig. They are (clovkwise from top right) USS Solstice (always liked the word), USS Bebhionn (Pronounced Be-veen, named for a moon in the Sol system named after a Celtic goddess), USS Rhodisia (name given by the game, just decided to keep it), USS Silmarillian (Tolkien fan here).