There are thousands of types of spiders (technically arachnids and not insects) crawling around the U.S., but only two of them–the black widow and the brown recluse–can cause serious problems, and even those are rare. Most of the time you’ll see red bumps that hurt and itch if you’re bitten by a spider. Very few people get the severe pain and cramping of a widow bite or the decaying ulcers of a recluse bite (although if you do, get medical help right away).
Most bites will have a small clear area in the center surrounded by redness that may or may not be raised. People tend to become more sensitive and have larger reactions after each episode. Reactions can include itch, swelling, rash and wheals (large round red area on the skin). Severe reactions can cause skin blisters and trouble breathing, although these reactions are very rare. 
The size of bed bug bites varies with a number of different factors. Bed bugs inject an anti-coagulant along with their saliva when they pierce the skin to take a blood meal. This anti-coagulant is mostly responsible for how a person reacts to the bite and determines the size of the bug’s bite. Since people will have various sensitivities to the bed bug’s bite, the size of the bite will vary, as well. Another factor that influences the size of a bed bug reaction is the number of times a person is bitten. Bite reactions of people bitten many times are also variable, and their response may be either more or less intense as the number of bites increases.