It depends on your definition, but I would assume we're not counting any outside sources (Gamesharks, DexDrives, or trading).
Gran Turismo 1: All prize cars could be re-won with exception to the license test cars. So the Dodge Copperhead road car, the TRD3000GT, and the Nismo 400R were that game's rarest cars, only handed out once per natural game. I'd say the TRD is the hardest to grab - the last license in every GT game tends to be easier to gold than others, since full laps give more leeway, and B was easier than A.
Gran Turismo 2: I think there were some series that only handed out prizes once, but I could be wrong. Otherwise, same as before - license test gold cars would be the hardest - but I'd say it's any of the "International" ones; IC, IB, and IA. B and A were doable, S was full-laps again, but these ones all had one or two incredibly hard tests per license (the Camaro blind corner test, the slaloms). That means the GTO, Del Sol, and FTO LM Editions were the rarest: most unfortunate if you wanted a specific colour. The Denso Sard Supra was rare due to a glitch: it was the prize for the Trial Mountain endurance race, but every so often, a Vector LM Edition would show up in that race, which was far faster than the regulations allowed.
Gran Turismo 3: Actually not the license test cars this time! If only because all of them can be won at least one other time in other races (the issues of having such a large career mode and such a small car roster). I'm pretty sure the F094/S awarded for 100% completion wasn't a unique colour scheme, so technically, the rarest car? The Aston Martin Vanquish - it could only be won twice in a regular play through.
Gran Turismo 4: The "Black Beauties" (787B, R92CP, R390, and GT-one) could be purchased infinitely, as long as you felt like throwing 700 game days at the goal, so they're out. I'd say the all-black Formula GT, since it was only available as a gift for completing 100%.
Gran Turismo 5: Not counting the specific region DLC bonus cars (seriously, one of my least-favourite things of this generation), and obviously ignoring trading, I suppose the rarest cars are the X2010 Prototype and the 370Z Academy car. The former for the skill required to obtain it, and the latter for it's... unique method of obtaining. Especially when, originally, you only had one Level 12 ticket to use.