What is the maximum altitude of barometric altimeters?
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.