I know of numerous vital corporate systems that were proven to fail in year 2000. The only reason they didn't fail was because they were very easy to fix.
Most of our databases were fine - SQL Server already used a 64 bit datetime structure that would store date/time to the millisecond from like years 1750-9999, and most other Microsoft programs used the 32 bit structure that will max out around 2038,so all Microsoft had to do was roll out patches that changed the default date conversions when people typed in 2-digit years - no biggie.
Some programmers however chose to use 6-digit character string or integer variables to store dates in programs where time messes up date calculations and comparisons though, because they were too lazy to trim time from the normal datetime variables when they displayed it or stored it in the database.
all we had to do was identify their DYI year and date of types, change them to standard datetime types, and search for every place they were used to correct the calculations and conversions.
One thing no one thought of was our backup software, which keeps the last 3 years of data online, and keeps 10 years offline but on a tape robot that could load history data online as needed, then takes it back offline after it's not accessed for three months or something like that.
Well, when y2k came, we installed and retested all the stuff we modified and then went home after working for like 48 hours straight.
Well, an auditor called us about 10 hours later, and said that history data was completely missing. So our manager runs down there and finds the silly tape robot in the process of securely erasing all its tapes and piling them in the destruction bin, since it thought the data and tapes was 2000 years old (or - 2000 years old which made it go wacko or something).
luckily there was a off site backup system that was manual, so most of those tapes were good, and the routine to get rid of disk-resident data was just sitting there waiting for the backup to happen. I think we lost like 2 day's worth of data because of bad tapes , which wasn't fun at all typing it back in from paper printouts, scanned for files still in temp files on PC's, etc.