Grand Theft Auto III
A major step up for the series, this game abandoned the top-down view in favor of the 3D third person shooter and driving style combo that reigns supreme today. Not only was there a significantly richer plot, voice actors like Michael Madsen and Frank Vincent were employed for the cast of characters. GTA III was also a lot more realistic and violent than the first two (this was the first game in which cop killing was encouraged), so many retail chains like Walmart began checking customer's I.D.s to ensure they met the 17 and over requirement.
Grand Theft Auto: Vice City
By far the prettiest GTA environment-wise, this version was set in the Miami-inspired Vice City in 1986. You played as Tommy Vercetti, a Mafia hitman who was recently released from prison in Liberty City. Gameplay was very open-ended, and you could cruise around in your stolen car listening to Flock of Seagulls to your heart's content. Your ten classes of weapons came in handy since you could now buy property such as boatyards, strip clubs, and an "ice cream delivery business."
irl
I bought a collector's edition of GTA 1, 2 and London a couple of years ago for £5.99 or some ridiculous sum like that, and I never ever worked out how to play it. I remember when it first came out everyone was raving about it, so there must be something good about it, but I found myself stuck in the first level, without even managing to complete one mission. The birds eye view really got me; the only ones I'd known before were the 3D ones that Richard (my boyfriend) played, and I was expecting the old ones to be the same.
Oh well. I have my playstation out again for the moment (I don't usually have a TV in my room because it makes it messy, so I only get it out for a couple of weeks now and then, mostly I play handhelds) so maybe when I finish Spyro the Dragon I'll try GTA again, see if I can work it out this time.