I'll avoid the obvious and go for some of my favourite of all time that never get mentioned:
Scarface
Like Vice City, but literally the thing that Vice City is copying. Go to the nightclub, listen to those iconic songs, deal lots and lots of yeyo.
War of the Monsters
The only game I know where you can properly have epic B-movie monster battles, with a completely destructible city (and more) where everything can be used as a weaponm just as you imagine it should be. 'Sequel' to King of the Monsters on Mega Drive (which I also had).
The Thing
I don't like horror games, but I played all of this. Try and keep your crew together and sane, and try and figure out if any of them are actually the thing... while also making sure no one suspects YOU!
State of Emergency
Rockstar's first game after GTA III exploded onto the scene, so it inevitably got panned, but I remember it being a lot of fun.
Godfather
Should've been terrible, was actually pretty good. Definite try for fans of Mafia. Godfather II was Battlefield/front-like dumb fun, but that's PS3.
This Is Football 2003
I wanted FIFA 2003, my mum got this... and it was actually way better. It had lower league football long before FIFA and Pro Evo did; actual seasons (rather than one league campaign) with players developing, aging and retiring; life-like faces; personalities and even the ref had a field of view - I remember Gazza getting revenge on me behind the ref by hacking me down off the ball.