Random Events in RPGs

What does everyone think about random events in RPGs? On the positive side, it gives more replayability, on the negative side, you don't get to see everything, you might miss beneficial stuff, etc.

I've been thinking about whether or not to implement them. Should they be one time random events, where the chance is only calculated once, and it either happens then, or doesn't happen at all.

Also, do you think that it should be decided whether or not it will happen right from the beginning, or when the event would fire (allowing you to load, do it, then load again if you don't like the outcome, and get a different one)?

Random events are very good, but they can be bad, so you need them but need to be able to have a chance to disable them.

Any particular reason for having a chance to disable them? Its for a single player campaign by the way. It's not like you can disable them in real life.

Well, in that case, it'd be better to leave em on.