I learned this from one of my high school teachers. I remember she had told my mom about how missionaries will sometimes carry large amounts of baking soda with them on their trips for many different uses. This is one of them, and it works surprisingly well if you use it right.
NOTES: Works best on fresh mosquito bites and will sometimes make them disappear altogether. Will work on older ones by diminishing their size and itchiness. Do not use on open sores. Will help with other insect bites, but will sting badly on certain types such as ant bites. You can try it, but don't say I didn't warn you. You may also use salt (equal amount) in place of the baking soda, but I don't remember if it works as well, and it may sting more. The baking soda method might sting a little, but no worse then Benadryl sprays, etc. Be patient. It's best to just leave it on until you forget it's there and the bite goes away. Once it does, you may wash the baking soda off with water. Recipe can be easily doubled, quadrupled, etc. Just use equal amounts.