One doesn't have to go that far. Mortgages, life insurance, annuity assurance and the like can run for more than the mere 23 years that are between now and 2038.
Heck, I won't even be retired in 2038 if things continue to work as they do now.
Apparently it already caused trouble with AOLServer in 2006 [0] because there was a database connection timeout of 1 billion seconds which hit the 32bit limit.
For example, if you're are a scientist you might want to calculate where planet xyz is in 100,000 years - and store that date on your computer, today.