I just came across a wonderful, all-natural, incredibly simple bug bite remedy while perusing the lovely blog Nonchalant Mom. Carina--The Nonchalant Mom--swears by applying raw onion to the bite as soon as possible, for about 10 minutes. The onion apparently mitigates the itching with lasting effect.
I've also found the (mostly) natural Quantum Sting Soothe to be effective itch relief, but it does require multiple applications. And it isn't as natural as a plain, unadulterated vegetable!
Of course, the best itch relief is not getting mosquito bites in the first place. This year, we've been using Swy Flotter by Kiss My Face. It's natural, DEET free and kid safe. It smells nice (it contains lavender and citronella) and has been extremely effective in our Connecticut back yard. The only downside is that it is fairly oily. But hey, I'll take a little greasy feeling for a natural and effective bug repellent.