Y2K was pretty much of a bust. I work with a number of small non-profits.
Two of them, in adjoining offices, took different approaches: One of them
hired a consultant and replaced older machines and spent money specifically
aimed at this issue--and discussed that effort in fundraising letters. The
other, which I was working with at the time, simply put into place
vendor-supplied patches and applications. The only place where we decided
to tough it out was a voice-mail system which wanted $1500 for a software
rev. After Janary 1, 2000, the days of the week were wrong on the phones
until we figured out which year to set the system to in order to get that in
synch, and, I believe, stored voice messages may have been lost. We
discussed this in advance with staff, and it isn't clear whether or not any
were lost---nobody noticed any problem, anyway.
So--yeah, some people will probably be late for church, or maybe even miss
planes, etc. I doubt that the world will grind to a halt as a result.