What is the maximum altitude of barometric altimeters? An altimeter works by sensing static air pressure. As altitude goes up, the pressure decreases. 

If I take a barometric altimeter up to space (e.g. up to satellite orbit), at what altitude does its reading become useless, i.e. the reading can no longer be trusted as a measurement of the height above sea level?

(While altimeter reading is different than GPS altitude even at low altitudes, it is still a very good measurement of height. I'm asking at what height, the air becomes so thin that it is implausible to measure altitude based on static air pressure?).
It depends on the altimeter's design and certification. An example for a  modern analog (aneroid) altimeter is this $5,000 Mid-Continent model.



Its certified range is -1,000 to +20,000 feet, this is a reading you can depend on. The actual mechanical range is -15,000 to +50,000 feet.

An RVSM altimeter working off multiple sources and an air data computer can take you higher. And an altimeter on an F-104 is probably even better.

A cheaper $150 model shows a certified range of 10,000 feet for one of the variants.