"Number one rule for fiction: Coincidence can be used to worsen a character's predicament, but never to solve his problems."
~ Vivian Vande Velde
Coincidences can be fun things to play with in writing. I don't think it's an easy device to master, but it can lead to some interesting outcomes. Like Vivian says, though, we can't use it to end our stories. If we have created effective conflicts and planned for effective resolutions, coincidence gets in the way at the end.
Above all, we must leave our readers feeling satisfied, with some sense of closure - if it's a series, then at least enough to carry us to the next book. Our MCs must make choices and experience conflicts and create their own outcomes. Using a coincidence to bring resolution to your MC leaves readers feeling cheated. And that is not what we want.
What do you think?