There is ultimately no such thing as coincidence because God is working in the world to bring about His plan.

We shouldn't write ourselves into dead ends and then use coincidences because we don't know what else to do.

Though, having said that, I have used semi coincidence in one of my novels. Though that was only a secondary solution to a semi-minor problem.

I think...though I haven't thought about this much...that the main difference is whether or not the accident or coincidence makes sense – whether or not there was some good explanation earlier in the novel for why it would happen. If there is that element of – foreshadowing, I suppose you might call it – then I am excited and surprised and (if I like the characters) really happy, rather than being disappointed.
If it is used for something too big, however (for instance, the climax of the novel), it feels like a cop-out still, even if it was foreshadowed. It's too important to be ruled by coincidences and accidents. (Unless, of course, it's a humorous work...in which case, accidents ruling the climaxes are great, if so desired. )

I've seen several quotes (none of which I can bring to mind in exact wording, alas) to the effect that the difference between truth and fiction is that truth is required to be plausible. Critics (and authors) also like to talk about the "willing suspension of disbelief." And readers tend to be more willing to accept implausible coincidences when they're making the protagonist's Problem worse, because they expect the author to get the protagonist out of the Problem by the end, than coincidences that make the protagonist's Problem significantly easier.