Definitely lots of exciting discoveries happen by accident--possibly most. But understanding what those discoveries actually are requires carefully designed experiments. In the absence of careful controls Occam's razor has to apply.
Scientific discovery often happens by accident, i.e. unpredictably. And when you're not expecting to discover something, you're obviously not being precise about it.
A concrete example is the accidental discovery of the cosmic microwave background radiation. If you Google "accidental discovery" you'll find hundreds of other examples.
Or, if you prefer an Asimov quote:
"The most exciting phrase to hear in science, the one that heralds new discoveries, is not 'Eureka!' but 'That's funny...'"