Summarize:

By picking two smaller bags (ie. a roller bag that can fit in the overhead bins and a backpack for under the seat) you eliminate having to check any luggage at all, and that also eliminates lost luggage and finding luggage at the baggage claim! However, if you are unable to carry-on your suitcase, some important things to remember are:  Most airlines charge per bag, so aim for big suitcases if you need to to cut down on number.  However, overweight bags typically cost more than additional bags, so be careful! Choose unique bags. You want to be able to spot it quickly at the pickup carousels. If you have a generic bag, put a marker like a ribbon on it. Aim for at least one roller. You can stack a duffel bag on top of a roller bag, but carrying multiple duffel bags is a drag. Check for damages to your suitcases/bags before you go. In the rolling suitcase, pack all of your clothes, toiletries, and items you won't need until you arrive. There are many different ways to pack, but many people find that rolling up your clothes keeps clothes from wrinkling and saves space in your suitcase. If you don't like that method, do some research to find other ways to pack your clothes. As you pack, check things off of your list to make sure that you haven't forgotten anything. Each passenger gets a baggage allowance, which is usually determined by fare, destination, date of travel and how frequently you fly. To make sure that your suitcase doesn't exceed the weight limit, weigh your suitcase beforehand. There are gadgets to do this for you, or you can use a bathroom scale. If you are having problems with your scale, first weigh yourself, then weigh yourself with the suitcase, and subtract the the weight of you alone. Find out your baggage allowance, and if you luggage exceeds it, consider taking out some items. As you're packing, make a list of things that you don't have or need to pack last-minute. If you don't have a travel toothbrush, or you had to use your phone charger the night before, write it down and put the note in a noticeable area for easier remembering. The day before your trip, plug in all the devices you will be traveling with, such as cell phones, iPods/MP3 players, portable game systems, digital cameras, and any other device that requires charging. Remember to bring your chargers with you if you think your devices will run out of battery while you're away. Your trip destination will determine the kinds of things to pack, and the length will determine how much of each item is to be packed. What days do you have special events planned? How can you use the same pieces over and over? If you can, try to avoid needing a checked bag. More and more airlines are charging for that first checked bag, and a cheap flight can turn into an expensive one in a matter of no time. If flight attendants can live out of a carry-on for over a week at a time, so can you. Checking before packing can help pinpoint what you really need. For example, Vermont typically has mild summers, but also has "heat waves" that can make it semi-tropical. Checking the weather will let you know if you really need to pack that tank top or that umbrella. Take a small amount of multipurpose items to deal with the climate of your vacation destination. For instance, one waterproof windbreaker takes less space than a raincoat and a jacket. If you’re going to a different country or overseas, odds are certain things will be different. Will you need an electronics adapter? You may not be able to bring your Saudi host a bottle of wine, for example. Or take certain kinds of plant seeds to Australia.
Pick out your bags. Pack it all up the day before your trip. Weigh your suitcases. Take care of last-minute items. Recharge all your essential devices. Know the duration of your flight and trip. Check the weather. If you are leaving your country, check if you need adapters. Understand prohibitions.