Splinter Cell (stealth, can be found for the mere price of $1.99 at gamestop)
Indigo Prophecy (story heavy)
Dreamfall: The Longest Journey (story heavy, technically a sequel, but you don't really need to know anything)
Star Wars: Knights of the Old Republic (Story heavy, RPG, must-get)
Silent Hill 2: Restless Dreams (horror, unique)
Ninja Gaiden Black (best action game last generation)
The Chronicles of Riddick (FPS, best looking Xbox game)
Psychonauts (something different, light hearted)
Beyond Good & Evil (its like Zelda, but better)
Pariah (FPS, story)
And of course, Halo 1 and 2 are a must; they're like default titles that every Xbox owner should have.
Everything I've listed are basically the best single-player experiences on the Xbox, both by critical acclaim and fans. Sequels are things to try later, such as KOTOR 2, and the rest of the Splinter Cells.
Though I'm sure there are more, that other people have listed, like Otogi, and Panzer Dragoon.