In North America, there are very few types of insects that carry venom or poison, and none whose venom is dangerous. However, it is possible for an insect bite or sting to cause an allergic reaction that can range from a mild local reaction to something like a severe asthma attack. In extreme allergic reactions, your airways can close up and you can even stop breathing.
The insect responsible for the largest number of severe allergic reactions is the yellow jacket wasp. Considering both multiple stings and allergic reactions to single stings, insects actually harm or even kill (in rare cases) more than three times as many North Americans as snakes do.