The back door originally didn't latch properly. When the side door on the garage got replaced, we had all of the outside locksets replaced at the same time, so we have consistent knobs and one key for everything. That improved matters, but didn't completely fix things: the deadbolt would not lock if the door was closed too firmly. Yesterday, I adjusted the striker plate and the positioning of the deadbolt, and fixed that problem.
The other issue was the upstairs bathroom: the latch would not engage properly there either, and the door would not stay closed. I finally got tired of that a little while ago. The problem turned out to be that the striker plate was a tiny bit too low, preventing all but the bottom corner of the latch from engaging. Five minutes' work with a cordless Dremel rotary tool with wood bit, and a couple of toothpicks to shift the wood screws upward, moved the plate up enough to allow the door to latch.
Everyone needs a Dremel tool. They're just too darn useful, not to mention affordable, not to be included in the average person's tool kit.