I replace the tires when I buy a used bike. Too risky if something goes wrong.

 

Like Gr said, tire manufacture date is on the sidewall, under 5 years old and good tread, and not a Dunlop 400 series or Chinese made, I'd consider getting some more miles out of them (I yanked a pair of Dunlop 400s with less than 500 miles on them). But I do pull the wheels anyway to check the bearings on a "new" used bike. That said, I've had too old tires on every used bike I've bought since the 70s and the only wheel bearings I didn't feel needed replacing were the roller bearings in my 89 and surprisingly the Russian Urals.

A lot of these newer sealed bearings leave a lot to be desired in reliability. Amazing how little attention so many people give to their wheels, lot more to it than just looking to see if there's any tread left (I've bought bikes with completely bald rear tires, too).