I was also raised to buy used vehicles. My parents bought a new car once when they were young and my Dad always told me stories about how he had to eat soda crackers with peanut butter for supper several times to make the payments and would never buy new again. The real reason we were always told to buy used was because the car depreciates by several thousand dollars as soon as you drive it off the lot. So why pay $3000-$5000 for a new car smell?
That being said, DH and I are currently driving a car we bought new (Subaru Forester). We fully intended to buy used, but between the new graduate rebate and the manufacturers rebate at the time (we have the last model year for the previous style of forester, so they were offering a $3000 rebate to get rid of the old models) it was actually cheaper for us to buy new than to buy a 2 year old Forester! If we were to finance, that also would have been a good reason (cheaper financing options on new than used.) So we did, but that's the only reason. So I think you have to do the math and see what makes sense for you.
We also have a '98 Dodge Laramie pickup truck currently that we paid $2700 for, and after driving it for 4 years (not daily mind you, but on some long trips, pulling a trailer, taking heavy loads to the dump, and through the Canadian Rockies) we've had to do oil changes and pay for tires, and that's it. Our truck before that was an '89 Chev that we paid $500 for and then drove until it died (we drove it for 4 years!). I drove my gramma's 1990 Toyota from 2004-2008 and had to get 1 repair: a new hose ($200). We sold it when the transmission started to go. Before that I had a 1989 Chev Cavalier, which required a few repairs along the way, maybe $1500-2000 in the 7 years I drove it (I got it when I turned 16 in 1997). I feel like ALL of those used cars were a great value and I will buy used again for sure.
I think that you have to do your research, check consumers reports and lemonaid guides, but depending on the vehicle, yes, used can be good value. Especially as if you are buying a "newer" used car, you can often still get a warrantly.
My good friend's hubby is a mechanic, and he says that in his experience, you will almost always spend less on a used car. Even if you have to get a repair for $200 every 3 or 4 mos, this is still cheaper than car payments!