My wife and I follow a pattern of paying off a car (after extending the payments overlong) then driving it a few years until small Gremlins start to show up. By Gremlins I don't mean that 70s AMC abomination, I mean "little problems that need a mechanic to fix."
In the meantime, we enjoy NOT having a car payment each month. Since we buy pretty expensive cars, that amount each month of "extra money" we use to upgrade something in the house, take a weekend away, etc.
A new car loses 20% per year in depreciation. So an 80k car will lose 16k in value in the first year. Think about that when you're NOT making those payments.