Insects bite for two reasons: to feed themselves or to defend themselves.

A few examples of the former are gnats, mosquitoes, bedbugs, fleas, lice and horseflies.

The others are much more diverse, and usually it is sound instinct to treat large insects, especially with large mandibles like the bigger ground beetles with some respect. Some true bugs can sink their proboscis deep in your thumb as well. If they do not feel threatened, however, they will probably walk freely over your hands without biting.