I'm sure some software will need to be re-written between now and 2038, but I don't think it will be quite as bad as Y2K just because that was only a 15 year gap (Sometimes less), whereas this is over 24 years.
I just think a lot of software will be naturally replaced between now and then. And while there will be a slight mad scramble to fix stuff at the last minute, I don't think it is Y2K-2.
See http://en.wikipedia.org/wiki/Year_2038_problem for a basic overview. None of this stuff is unfixable. But it is a real problem, and tracking it down will be hard.
As far as I know, the only major operating system that has dealt with Y2038 is OpenBSD [3].
[1] - https://github.com/opensource-apple/xnu/blob/bb7368935f659ad...
[2] - https://github.com/opensource-apple/xnu/blob/bb7368935f659ad...
[3] - http://www.openbsd.org/55.html , http://www.undeadly.org/cgi?action=article&sid=2013081307224...
I doubt this will be a real problem in 2038, then again the prevalence of computing devices is much larger now and will continue to grow by 2038, but so will technical aptitude, so hopefully they'll cancel out and this will still not be a problem.