If I replace a worn or old tire, I always replace the tube also. I don't get many flats so my tubes get old and cranky just like my tires. Last week, one had a thin spot from wear inside a well-used tire.

Also, I'm lucky enough to have several bikes so I don't put a lot of mileage on just one bike. The tires can get brittle and the sidewalls crack from age, the dry heat or the ozone in the garage produced by the furnace, water heater, etc. It just isn't worth it to do one without the other.

So, it just depends on your riding and bike storage situation.