How long do magnetic tapes last?

So far so good, 60 years later, many tapes that were recorded in the 1950s are continuing to perform excellently.

Do old reel to reel tapes have any value?

Prerecorded commercially made tapes by the record companies are the most valuable, sometimes reaching prices of over $1000 for a single album recorded on a 7 inch reel. Blank tape produced in the 1980s and 90s by TDK, Maxell, BASF, Quantegy and some other manufacturers still remains sought after now that current tape formulations have become quite expensive with very little competition in the industry.