Star Trek Voyager: Elite Force.

• It's a first person shooter from a venerable studio in the genre, Raven Software.
• Put out during their "golden age", before Wolfenstein and Singularity flopped and uncle Bobby sent them to work in the Call of Duty mines.
• Really cool selection of sci-fi guns, some of them pretty unique.
• Campaign is essentially a prototype for Quake 4. It was built by the same internal team at Raven.
• It has a more interesting story than Quake 4.
• It's an early example of a game that lets you choose your sex. NPC dialog changes to reflect this.
• The whole cast of Star Trek: Voyager lends their voice talent to the game, including Jeri Ryan.

It also has a sequel, made by another studio. Elite Force II isn't quite as good, but it is still worth playing if you like the original. It loses the female protagonist option, likely because it was 2003 and the story had a love triangle. It's a visual powerhouse though, really pushing the limits of the Quake III engine far beyond what many people likely thought possible.