Okami-completely different from what you've seen or heard! an awesome, fun action/adventure that has a bit of old school flava!
Metal Gear Solid-deep story line, fun gameplay, relatively intelligent AIs, an espionage/sneaky around with lots of personality! (best to start from #1-#3, but #1 is on the gamecube as a remake (only graphic wise, very good! and the original is a hard to find PS1 title)
Tenchu-great ninja game that's fast paced and fun to play! standard level complition and a cool boss battle at the end! (i've only played #3, but i hear #1 and #2 are great too!
Way of the Samurai 2-lots of customization, multiple endings and battle anyone with a sword! awesome! awesome! be good or bad or just a wanderer carried by the wind!
^_^ there's also Grand Theft Auto for a great shot 'em up with some surprisingly creative story to it and Bully... haven't played it but heard it was pretty much one of the best things ever!
these were all for the PS2! you'll have to specify if you want other systems
p.s.: Growlanser is also a great old school feeling RPG (different from final fantasy) it comes it a pack of the #2 and #3, while #1,#4 and #5 haven't gone state side... T_T the two pack was made by a now dead company... TTT_TTTT