Cars last an average of 13 years these days, obviously some last a lot longer, typically up to 20 years. It's not just low mileage you need to look for, a full service history is essential preferably from a dealership garage (not a random back street grease monkey). The older they are, the more important to do a long test drive to get the feel of the suspension, gear box, clutch, steering, etc., to make sure it "feels right". Even low mileage cars may have been driven badly, i.e. regularly mounting the kerb etc which can cause excessive wear and tear on steering and suspension, and poor driving can cause clutch and gear box to wear out sooner.
As for whether at 13 or 18 is better, how long is a piece of string. If the 13 one has low mileage, FSH and has been well driven, it could well be in a better state than the 18 one.
One of our cars is a 15 year old Citroen C3 and it's still in immaculate condition, FSH, and in excellent mechanical condition, never broken down and no repairs other than routine servicing issues, i.e. tyres, brake pads, spark plugs, a battery, timing belt, etc. Still drives like a dream, clutch, gearbox, steering and suspension still feel smooth. You see an awful lot of C3s on the road from between 2003 and 2009. As a PP said, it does depend also on the make and model - some cars are a lot cheaper and easier to maintain than others. And also the "simplicity" of the car - the more bells and whistles, the more there is to go wrong. If I was buying an "old" car, say 10 years or so, I'd steer clear of top of the range models and stick with a car that's simple, basic and popular so that there's less to go wrong and more likely to get cheaper parts etc.