It's 2038, not 2037.[1] (Specifically, January 19th, 2038 at 3:14:08am.) And while lots of systems will be 64-bit, many programs still won't be -- and it seems highly likely that this will be a significantly more serious and widespread problem than, say, Y2K or DST. (And certainly more serious than leap seconds, which happen relatively frequently.) Then again, I might be biased: perhaps I'm secretly hoping to spend the years leading up to 2038 paying for my retirement with high-priced consulting gigs to fix it...
[1] http://en.wikipedia.org/wiki/Year_2038_problem