We tend to buy new (or very nearly new, i.e. ex demos) and keep them till they drop which is usually in the 10-20 year range. But we look after them, i.e. have them serviced to schedule at dealership garages and are careful drivers (i.e. no bumping up/down kerbs etc), and we buy "sensible" cars, i.e. common makes and mid range models etc which are cheaper to repair anyway.
Depending on our travel/commuting, they either get to very high mileage or very old. Highest mileage was around 195k when I was doing a long daily commute. Oldest is one we currently have which is 17 years old and still going strong and still immaculate - no dents/scratches and the interior is still pristine. It actually got written off a few years ago after a moronic neighbour left her handbrake on, but we bought it back from her insurers and financed the repairs out of the insurance payout - we couldn't let an immaculate low mileage car go to the scrapyard! (We actually made a profit on that as the insurance payout was higher than the repair shop cost!).
Never really had any stupidly expensive repairs and none have been particularly prone to breaking down. Never needed any new gearboxes, clutches, etc. Usually just a new battery if the car gets to around 10 years old, then consumables such as tyres, brakes, spark plugs, etc. Occasionally, we've needed something like cheap suspension parts (boots? arms?) picked up at the MOT. I think probably the most expensive unscheduled repair was a replacement heater/cooler blower fan where the cost of the motor itself was cheap but it took the garage most of a full day to take out the dashboard to get to it - I think it cost around £750, but the car was around a decade old, so not too bad,
When we were a lot younger, we'd buy second hand cars - typically 3-5 years old, keep them a couple of years and replace, but we always chose low mileage with full service history and never had problems with those either.
For us, buying new is the most economical way of financing a car, simply because we keep them so long. Leasing/replacing every 3 years or so is a very expensive way of having a car and is more vanity than sanity.