We bought a 10 year old used van private party recently and before going to look at it asked the owner if he minded us getting it inspected. He didn't, so we set up a pre-purchase inspection appointment with the mechanic. We told the mechanic if we didn't like the van we'd cancel the appointment and he was fine with that. The owner let us test drive the van alone, all he wanted to see was our license and proof of insurance. So we drove it, liked it, took it to get inspected during our test drive. We knew it needed $1000 in maintenance (timing belt, etc.) but the inspection also revealed another $2000 in needed maintenance. We showed the owner the inspection paperwork and he came down another $1000 and we bought the van. In this case, the $80 inspection really paid off. And this was a very well-maintained 2 owner van; the owner had all the maintenance records, etc.
One time we were interested in a used SUV from a Toyota dealer. Usually we like to stick with one or two owner vehicles (and we prefer to buy private party so we know more about its history). But we could only find this particular vehicle for sale at dealerships. So this SUV had had 3 or 4 owners and we felt like we knew nothing of its history, other than a few maintenance records on carfax. We liked it but told the dealer we wanted to have it inspected before buying. They let us drive it to a mechanic and it turned out the vehicle had lots of problems, one of which was an oil leak that the dealer had tried to cover up! Needless to say, we passed on that one. Again, the $80 inspection was well worth it.
We have purchased a vehicle private party without doing a pre-purchase inspection but it was a newer vehicle (only 2 years old) with only 25,000 miles and still under warranty. It was a one-owner, a very nice elderly couple, and they had all the maintenance records. So we really weren't worried. We actually didn't even test drive it! (we'd test driven the same car at a dealer a few days before so we knew we liked it).
Kind of funny--one time my husband went to test drive a $33,000 SUV that was for sale private party. He drove up in our crappy 13-year-old vehicle and the lady just let him drive off by himself in her expensive SUV! I couldn't believe it when he told me later; I thought for sure she'd want to go along with him while he drove it.