I haven't played too many First Person Puzzle games but Portal sure stands out amongst the crowd of shooters. You do not shoot enemies, you do not throw grenades, you simply make portals with your portal gun to get from point A to point B. Sounds simple but as the levels go on, the puzzles just keep getting harder.
Puzzles are completed usually by getting to point A to point B with many obstructions and obstacles in the way. Puzzles can be solved in many clever ways and each puzzle seems to test reflexes and skills in problem solving.
The narrative surrounding the game is top notch. You initially find yourself in a resting containment chamber (read: holding cell) and find out that you're the subject of an experiment by the menacingly polite, malevolent, passive aggressive, sarcastic super computer named Glados in which she gathers data from your successes or failures with portal technology. This story finds its way tied in with the Half-Life 2 main story which makes it even more tantalizing to the Half-Life 2 fanatic.
Portal is an excellent game that will bend your mind to think about first person shooters in different ways and cause you to start thinking with portals.