Don't forget you have Y2K38 coming up. Whereas Y2K was all about mainframes and old databases, Y2K38 will be older embedded equipment. Less impact if it goes bad, but there's no way to predict everything it'll affect.
Mainframes and old databases? It was 98/99 not 88/89. I spent all my time updating Netscape navigator, Windows and Java in my IT job for a fortune 500. I'm sure someone was still running crazy old stuff, someone always is, but it was solidly the age of the internet by then. I had a cable modem by that time.
With regards to old databases, they were used by tons of small businesses and industrial users. If a flour mill had a system written to track bulk shipments in 1992, you can bet it would still be in use in 2000. Fortune 500 companies run mostly off the shelf software and keep it up to date, but the SCADA system that runs a factory is a different story.
As far as mainframes go, the financial and manufacturing industries still use them. Quite a bit of the infrastructure we rely on even today is written in COBOL. It's easy to miss because the mainframe community is almost completely separate from the rest of the IT world, but it's there and even with IBM's push to get everyone on Java it won't be going away any time soon.