If the airline overbooks your flight and you are involuntarily bumped, that's another story. Then you do have specific rights that are guaranteed by federal law. First the airline will try to find volunteers willing to give up their seats in exchange for compensation. If that doesn't work, typically the last passengers to check in are the first to get involuntarily bumped. If you are one of them and the airline manages to get you to your final destination within an hour of your originally scheduled arrival time, you get nothing. Sorry.
But if the airline cannot get you there within two hours of your original arrival time for a domestic flight and four hours for an international flight, then the airline must compensate you. That reimbursement rate just changed and is now capped at $400. If your arrival is delayed more than that, you can be awarded up to $800.
If a flight is overbooked and you volunteer to give up your seat, usually the airline makes a standard offer, but actually the compensation is negotiable. If lots of people volunteer, the airline will choose the people who make the most modest demands. But if you can tell that the airline is having trouble getting enough volunteers, that's the time to go for the jugular. Most airlines offer a free round-trip ticket. Ask if you can have one without an expiration date. Without blackout dates. Without regional restrictions. Heck, ask for one that lets you fly to another country. For that matter, if you'd rather have cash, put on your poker face and demand money.
If an airline loses your luggage, don't immediately despair. Airlines are actually pretty good at finding people's suitcases even if "many bags look alike." Just think, you won't have to lug the thing, because most airlines deliver lost bags to your door. Years ago, when I was backpacking in Europe, an airline misplaced my big, grungy backpack in Zurich. I was on my way to a tiny town in the Alps that was hours away by train. Sure enough, the airline somehow arranged to drive my pack up the mountain and delivered it a couple hours after I arrived at my hotel.
If you are not so fortunate, the airline is required to compensate you for the loss of your belongings. The domestic limit is $1,250. The international limit is $9.07 per pound up to a total of $640 per bag. Be prepared to prove the value of the items you packed. Airlines compensate you for actual value only, not replacement value. If your suitcase is damaged in transit, most airlines will pay for repairs or pay to replace it. Same goes for the items inside, although the airline will balk if the contents broke while the suitcase itself appears unscathed. There are important exceptions you should know about. Most airlines post a list of excluded baggage they will not cover. Watch out. Electronic equipment is a common one and includes laptop computers.
DO YOUR HOMEWORK:
Find out whether the flight you're considering is typically on time. Flights early in the day tend to have a better record because there's a domino effect in delays as the day goes on.
Ask for compensation if your flight is badly delayed or canceled, even though you have no legal right to it.
If you opt to change carriers, get the old carrier to "endorse" your ticket and try to get the new carrier to match the fare.
Arrive early so you won't be involuntarily bumped.
If you are bumped against your will, make sure you get the compensation guaranteed by federal law.