You can find a chart of the five standard luggage sizes on the luggagepros.com page. These sizes start out with carry-on sizes and go up to the largest suitcases.
Most airlines require carry-on sizes for luggage to be 18"-22" or below. Anything larger than 22" is unobtainable throughout the flight. Passengers must stow larger bags under the aircraft and check them until the aircraft lands. The only luggage that passengers can access on any flight are carry-on bags. Most airlines allow one carry-on bag and one personal bag such as a purse, small backpack or diaper bag free of charge. One checked bag is allowed per person and all others usually require a fee.