As
@Owen Lucas said, it depends. Both of the cars in my garage have rebuilt titles. I have no regrets for either.
There was a time when I was in the run away camp. But a friend of mine, who is very successful, and has owned some very nice cars, has bought rebuilt title cars for each of his children's first car. He shared with me that he never regretted any of the purchases, and would not hesitate to recommend rebuilt cars to others.
But he has always bought from large reputable dealerships that specialize in rebuilt cars.
Although sideswiped, a PPI on my E350 found nothing that was out of the normal for a car of it's age and mileage and type. Both driver side doors were replaced, and if someone pays close attention, on the inside of the door you can see the paint line, where the original color just barely shows. This is a minor cosmetic condition that I'm willing to live with. Tires only last about 35k miles on the car. I've attributed this to the accident, as the alignment is just barely in spec, even after I had it worked on. But from talking with others that drive the same model, they only get about 40k miles out of a set of tires. This particular model seems to be hard on tires.
My wife's X5 was a flood car. The original owner drove through standing water. From the report I read, it never hydro locked, but was running poorly when it was taken to the BMW dealership. All fluids were replaced, the main battery was replaced. That's it. I carefully inspected the car before buying it, and am convinced that there was never any water intrusion into the cabin. February will be a year of ownership, and we have had only one problem with the car, and that problem was unrelated to the "flood damage".
I saved about $7k-$8k on the X5 vs a clean title with the same trim level and mileage. With the E350, I didn't pay much attention to the $ savings, but instead noted that I got a car with 40k miles on it, for the same price that other E350 4Matic Sport cars were selling for, with 80k-100k miles on them.
I said no regrets, but there is one. It is very common with salvaged title cars, to only get one set of keys. Both of mine were like that. No big deal with most cars. But a replacement key for the E350 is about $400-$500, and one for the X5 runs about a grand. And there is no aftermarket key option for either. Dealer only. I haven't ever got a second key for either yet. So there is that.
Would I buy another salvaged title car? Yes. But I would take the same careful measures that should be taken when buying any used car.