I too like older cars with low or reasonable mileage.
Rubber parts like window trim, belts, gaskets, hoses, and interior trim pieces may have dry rotted as a car reaches the decade old mark.
An older car with a timing belt should probably have the belt replaced even if the mileage doesn't indicate it. Expect the engine to develop a few oil leaks around the oil pan or valve cover, just from seal deterioration.
A particular concern is whether the coolant has rusted out the head gasket inside the engine. Coolant breaks down over time and becomes more corrosive. If you open the radiator (before test driving the car and warming up the engine, of course) and see a lot of rust inside, the head gasket is probably at risk. A car that has been owned by someone who didn't drive it much (e.g. grandma) might not have been maintained much either, so the coolant could be original. Some older cars end up requiring a top end rebuild at <100k miles because it has sat rusting from the inside.
Low mileage old cars may also have old tires. At about 5 years of age, the rubber becomes brittle and develops cracks. Even if they have good tread, old tires can start to seep out air and due to the brittleness they don't have as good traction. Expect to replace the tires before they wear out if you see lots of cracking.
Beware of otherwise nice cars that have "been sitting" and won't start because the fuel in the gas tank, fuel lines, filter, and injectors can go bad after 6-12 months. It can be very expensive to flush a fuel system and there's towing involved.
At the 15-20 year old mark, it's not a bad idea to buy a bunch of bulk rubber tubing and replace all the vaccum lines, one at a time. These can develop tiny dry rot cracks and cause perplexing and hard to diagnose issues. Some preventative maintenance here can head off some of the most common car problems later. Also not a bad idea to clean the air flow sensors with a spray can you can buy from the auto parts store. This job takes 15 minutes for an untrained monkey to perform.
Finally, THE most common reason to find an older car with low mileage is because the car was wrecked, stored for a long time, auctioned, and repaired. This process can take years to complete and in the meantime the car isn't racking up any mileage. I do not shy away from cars with previous damage or salvage titles. In fact they're usually a great deal because you can expect to pay 25% less. But if you're looking to pay full retail price, inquire about the title status or do a carfax before making your offer! It's awkward to back out when people or dealers spring this detail on you, but if that ever happens you should back out or lower your offer 25%. If they say "but you just committed to this price!" take a walk and never come back.