For my single player games, usually on.
For my multi-player games, I have done both.
I haven't seen these two events everyone is describing, however, With all of these mods available, surely, someone could edit out the extremely bad ones.
The free pastured cow or tornado'd tile is more like the seemingly randomness of nature, considering Civ4 doesn't deal with air currents, water temperature, frontal boundaries and el nino effect data. If, Rome gets the free cover promotion, I adjust my strategy to the new situation. I might attack their neighbor and save the Romans for my Rifleman attacks. So, most of these events I like, and do add flavor to the game.
However, I found one reciently, that is just lame. The slave revolt came up, and I didn't have enough to pay to stop it, but, didn't want to lose the 2 pop. So, I chose something that pushed aside temporarily, with a chance that it could come back. It did, but, my gold didn't go up, so, no matter how many times I tried, I couldn't save the 2 pop. I think, that part is lame. What is the point of putting it off for the next turn, if, we can't earn enough gold to pay off the revolters? I did have 3 revolts in 1 game, within 20 turns of each other that lasted a combined total of 7 turns. Lame, because, I was playing a Spiritual Leader, who's big advantage is normally not seeing revolts.
Note to others: I switched civics off of slavery after the revolt occured and I postponed it, and it still came back the next turn. So, getting off of slavery will not discontinue the event. Lame, you would think ending slavery would be enough and you wouldn't be forced to lose 2 pop.