In my experience, the most annoying culprits on squash are larger bugs--
Cucumber beetles (there are two types) are beetles with hard wing cases, yellow to greenish with stripes or spots. They are little buggers to catch in the heat of the day, but the best time to douse them in a sudsy bucket of water is in the evening.
Squash bugs are shield bugs, related to stink bugs. Their nymphs are small and strange looking, and they move a bit distinctively. the most satisfying thing to do with them is squash them.