-difficult-to-heal places, like fingers, face, over joints are good candidates.
-any time that a cut is gaping open - that is, that the flesh and skin is actually pulling the cut open - is a good candidate for stitching (or maybe steri-strips). especially if you can see muscle or fat.
-if it won't stop bleeding. that one should go without saying.
quite frankly, if you've got health insurance, there's no reason not to go to an ER except for time and inconvenience. deep cuts can harbor infections, and they really, really suck. same goes for punctures.