For carry-on luggage, the TSA has established what it calls the 3-1-1 Rule: all carry-on liquids must be in 3.4-oz. containers or smaller, you may only carry one quart-sized bag of liquids, and one bag must be presented to TSA officers when going through airport security. The bag must be a clear, zip-top bag, and it must be quart-sized--a larger, partially-full bag is not allowed. Be sure that you present your bag of liquids when you go through airport security, rather than waiting for the officers to find it in your carry-on luggage. You will save time for everyone in line and make the process go much more smoothly.
Many different things constitute a liquid, according to the TSA. In addition to traditional liquids (water, mouthwash, etc.), gels--such as toothpaste, shampoo, etc.--are also considered liquids. Aerosols also fall under the classification of liquids; this includes hairspray and deodorants. All of these items must be among the items in your one quart-sized zip-top bag, and as previously mentioned, they must each be in containers that hold 3.4 oz. or smaller.
Exceptions can be made for some liquids. Baby formula, breast milk, and juices for children in containers larger than 3.4 oz. can be allowed by TSA officials, after screening that they find appropriate. Other exceptions to the 3.4-oz. rule are liquid medications and water or juices for people who require them because of a medical condition. Frozen items are allowed to be carried onto planes, as long as they are frozen solid. If they are slightly melted or slushy, then they must conform to the 3-1-1 rule.
If you are checking luggage, it might be easier to simply pack your liquids in your checked luggage. Liquids in checked luggage do not have to conform to the 3-1-1 rule. Although certain items are forbidden to be taken on planes at all, for the most part you can pack liquids in your checked luggage without fear. Your full-size toiletries and other liquid necessities in your checked luggage can be in whatever size container you need them to be.
There are some items that are prohibited on planes, regardless of what size container they are in. Aerosols that are not hairspray, deodorant, or other personal care items are not allowed. Also prohibited are any kinds of fuel (cooking fuels, for example), gasoline, and lighter fluid. Basically, if you have any liquid in your luggage that is flammable, it will likely not be allowed to accompany you on the plane.