Metal Gear Solid 3
I'd recommend the limited edition Subsistence re-release but they are quite hard to find + more expensive though the 3D camera makes it much more user friendly to gamers who are not so used to classic MGS controls (the camera always points north).
but yeah, it is a really original MGS game and has great re-playability especially with increasing difficulty, all the camo unlocks, easter eggs and hidden weapons and special items. No alternate ending though

Overall I'd say it's the second best MGS game next to the original MGS1. It also has a fun mini-game based on Ape Escape.
Resident Evil Code: Veronica-X
Hmm, don't have a Dreamcast? Well the PS2 version is just as good and could be considered the last "classic" Resident Evil game before RE4 and RE5 when all third-person-shooter, RE4 is still one of my all time fav games but I like the classic Resident Evil (you can find more of that on Gamecube with the RE1 remake plus Resident Evil Zero*). not so much re-playability though but it's a fairly long game with all the puzzles and intrigue and separate intertwining story-lines.
Red Dead Revolver
LOVED this game and especially the spaghetti western feel, it also is good for re-playability as you keep weapons + money from 1st playthrough where almost certainly you have not reached level cap in one playthrough.
I'd also recommend the Tomb Raider games but you're better off getting them on PC or 360 than PS2.
*RE4 is best played on Gamecube BTW and with HUGE replay value as you keep weapons, money and unlocks every time you complete and re-play a game. Gamecube consoles are dirt cheap, get one with a Component (RGB) cable and play on a HDTV... quality overall I'd put as in between 6th gen and Current Gen. VERY worth and and sorry I know this is a PS2 thread.