I have an 85 that had several problems when we got it, but that is why the last person wanted out of it, I have worked through them one at a time, none were really expensive mostly minor and most are the result of neglect of proper maintenance, and most problems probably fall into this catagory, if you sense a problem have someone that you trust that knows Corvettes have a look at it and try to keep ahead of the little things and most likely you won't have big issues. Remember these toys are still mechanical devices.

Trick question. As many of the respondants above said, we are talking about cars that are 14-25 years old.
Any thing mechanical and as complex as a automobile is and will breakdown regardless of how rigid a maintenance routine is kept up.
Mine is 1985 with 105,650. I bought her in February of last year and within 2 months of owning it had to replace the radiator, as it developed a pin hole leak. Found the date code on the old one to indicate it was original. Another couple of months after, I needed 4 tires... couldn't afford all 4, so I bought 2 during the summer and delayed buying the other two near the end of the year.
Before the tires, the A/C compressor died on me.... so I made a total system conversion to R134A while at it.
Right after the new year, my tranny started giving me issues. I stalled the repair a couple of months by replacing the TV Cable... but I couldn't escape.... rebuilt tranny in March-April. The list goes on.
But over all? for a 24 year old car, I am most pleased with how it runs, and it is a keeper for me.

i bought a 92 vette 3 years ago no problems at all runs and lookes great 60,000 miles on it now