You are allowed one carry-on bag and one personal item such as a purse or computer bag on each flight. Airlines differ on the size of carry-on baggage that they allow. However, the size is typically no larger than 22 inches by 14 inches by 9 inches and can usually weigh no more than 11 pounds.
Like carry-on baggage the exact sizes allowed are based on the particular airline you are flying on. With this in mind, the general size allowed is a combined height, legnth and width of 62 inches and not more than 50 pounds.
If you must pack luggage that is heavier or bigger than the guidelines set by your airline, you should expect to pay a fee. Typically, bags can be no heavier than 100 pounds or larger than 115 total inches.