1) Antihistamine
A great home remedy for mosquito bites is to take a tablet that is meant for hay fever and then to apply some eczema cream to the bite.  You should instantly feel relief.
 
2) Mouthwash
My favorite home remedy whenever I have a mosquito bite is to soak a cotton ball in plain mouthwash, and then allow some of the excess to drip directly onto the bite.  You'll find that this might sting a bit, but you'll soon feel relief.  If the itching doesn't immediately stop, you can press the cotton ball directly onto the bit and the itching will quickly subside.

Mosquito bites

3) Tea Tree Oil
A great natural remedy for mosquito bites is tea tree oil.  This can be applied directly to your bite for relief.  This natural oil works very well because it actually sterilizes the bite and will numb it as well.  Tea tree oil is great for mosquito bites, mite bites, flea and spider bites and bee stings.

4) Aspirin
A crushed aspirin mixed with a few drops of water makes an excellent homemade paste to use to treat mosquito bites.  Apply the paste to your bite and then cover it with a bandage and allow the paste to soak into the bite overnight.  This always works perfectly well for me.  You can also do this with baking soda and deodorant (not together, of course!).  Both of these home remedies work well, too.
 
5) Tobacco and Suction
All my life, I have used tobacco, vinegar and baking soda home remedies when faced with rashes, itches, and insect bites.  This is especially helpful when bitten by a mosquito.  When this natural remedy doesn't completely work, then you know that you have to remove the venom from the bite.  To accomplish this, I'll use a small vacuum pump (I have one for some minor car stuff) and I center the suction end over the bite and allow the vacuum to remain there for about one minute.  This will pull the venom out of the bite and you will instantly feel relief.
 
6) Baking Soda
Simply rub a small amount of baking soda onto the bite.  This will help to alleviate the itch and helps the bite to heal faster.