Today I got volcano that destroyed 2 or 3 towns (in a science city no less) with no way to protect them, that was really annoying (takes how many turns to rebuild?).
I haven't played many BTS games, the only quest was to build 11 triremes when I was playing France in RFC. No point since caravels were a better naval force at the time.
The best event I had was +1

in my planned production city when I built my forge (first forge built in my game). So many of these events are so situational. I had the Johnny Appleseed one (forest and +1

on the plot, outside of my BFC (was a few free hammers and a job for the worker waiting around to build railroads a little while later).
A couple questions about random events:
I repeatedly got the event wanting me to send resources to brothers of the faith (most of the time against the person who was gearing up for war against me, and repeatedly stopped by my AP, while at war with a civ they couldn't reach). Every single time there wasn't a resource I could select. Not even resources they could clearly use and had no access to (in one case I stopped sending Joao iron the turn before, and I could have traded it to him that same turn).
I also had hurricanes, but I was never sometimes not given the option to lose population (even on my size 20+ cities), while occasionally I did with rather small cities. Really sucked, when I had huge food supplies and little production.