GTA III hands down. That game has something magic about it that Rockstar couldn't replicate again, even if they tried. It MADE Grand Theft Auto.
It's just a damn shame it gets so much hate because "I can't get a haircut" or "It's not about the hood" and all the other BS that comes with people introduced to the series with San Andreas.
It doesn't help that the driving kinda sucks, the auto-aim locks onto grandmother's rather than the guy shooting me or my preferred target, it has shoreside vale, the story is one of the worst I've ever seen, has some of the most annoying/not fun side missions ever (Drive into the checkpoints with absurdly short timer ... hooray!), vans roll over at the slightest turn, and I can lose health by running down a hill.
GTA III is good, but we overlook a lot of its flaws because it was the first 3D GTA. It had a ton of flaws. I recently played it to 100%, so I'm not talking without experience. It's probably special because even if it wasn't your first GTA it was probably your first 3D GTA. I don't get that 'something special' for it. For me it was Vice City until IV took over the spot.
My list (as of today because I'm likely to change my mind about the specific placings below #2 on a whim.)
#1: GTA IV
#2: GTA VC
#3: GTA V
#4: GTA III
#5: GTA SA
#6: GTA LCS
#7: GTA VCS
#8: GTA A