I am a HUGE fan of games that require stealth and espionage and secret service stuff like that. The one game that got me hooked on this is Goldeneye for N64. I would just keep replaying the first stage and the two snow-stages over and over again because I LOVE the feeling of sneaking around, wreaking undetected havok. I'm going to list some games that involve (heavily) the stealth aspect and I ask you to add to it with other similar games. Thanks!
Goldeneye; N64
Metal Gear Solid; PS
Tom Clancy's Splinter Cell; PS2
Tenchu: Stealth Assassins; PS
Tenchu: Wrath of Heaven; PS2
SOCOM: U.S. Navy Seals; PS2
SOCOM would be a perfect example if only the sniper cross-hair didn't weave so much.