Long is the list of (rather compelling) reasons not to check your luggage at the airport, and compassionate am I in my convictions regarding this topic (been watching a lot of Star Wars recently). Right off the bat, it means you are probably bringing too much, and unless you are bringing equipment for the express purpose of engaging in some activity (surfing, sword fighting, arms deals, grave robbing), it is incredibly likely that you are bringing too much. So, let's get down to business, you should never check a bag at the airport because it:
COSTS YOU MONEY
Most airlines charge between $15 and $25 dollars for your first checked bag and $25-$45 for your second (if you're taking more than two checked bags, then you had best be moving). For international travel (that is, outside the United States), many airlines do not charge fees for your first checked bag, but charge anywhere from $30 up to $100 for your second. It varies greatly between airlines, so be sure to check your airline's website for details. Also remember that these fees apply to your outbound AND return trip. Airfare Watchdog is a useful site for baggage fee overviews.
However, please note that Southwest and JetBlue do not charge baggage fees on your first checked bag (or your second for Southwest!) within the US.
INHIBITS YOUR TRAVEL PLANS
This might not be obvious at first, but I have had enough cancelled, delayed, or rerouted flights to know that being tied to a bag under a plane somewhere can keep you from reaching your destination. Say you are in between flights waiting to catch your connection and all of a sudden your flight is cancelled or delayed. If all you have is a carry-on, then you can usually have yourself moved to another flight with the same destination (or a nearby destination), but if you have a bag under a plane somewhere, then you fall victim to the will of the airline (which means more waiting and more frustration).
See: TRAVEL HACKS: At The Airport, for more on airport strategy.
RISKS YOUR BELONGINGS BEING DAMAGED, LOST, OR STOLEN
By taking adequate precautions (carrying on valuables, packing intelligently, and, oh, not checking a bag in the first place) you can usually avoid having things damaged, lost, or stolen. However, even if you have nothing valuable or fragile in your luggage (thus curbing the likelihood of theft and damage), once the check-in counter swallows up your bag, that luggage becoming lost on its way to your destination is completely out of your control. An airline losing your luggage can ruin any trip (especially if you are not planning of staying near the airport for long), and even if your luggage is returned to you there is no making up for lost time.
FORCES YOU TO ARRIVE EARLIER AT THE AIRPORT
Even though this is a minor inconvenience, it still adds additional restrictions to your travelling. I have known people to miss flights because they did not arrive in time to check their bags. The check-in times are recommended by airlines are usually 90 minutes for domestic flights and 120 minutes for international flights (with the baggage cutoff hovering somewhere around 45-50 minutes before departure). Personally, I tend to shave about 30 minutes off those suggested times (without a check-in), and my record for catching flights remains untarnished.
Sometimes something as simple as oversleeping, as mundane as traffic, or as terrifying as a kidnapping can cause you to run late to the airport; don't let your baggage keep you from making your flight.
MEANS YOU MUST WAIT AT THE BAGGAGE CLAIM
Don't think this is a reason not to check a bag? Think again. You stand around waiting for your bag to materialize while suppressing the nagging idea that it may never appear. You cannot help but wonder why these people need to rush to grab their bag as soon as it pops out of the magical luggage portal, and you slowly being to hate everyone around you. I mean honestly, they can't just wait thirty seconds for your bag to come around to them? Did they really have to push Nana's wheelchair out of the way so that they could get to their bag that much sooner?
You also risk longer lines for a taxi or bus. Having someone pick you up? If you have to wait for bags there is no telling how long after your flight lands you will be ready (“Sir, there is NO waiting at the curb”). And if they park? Well parking is rarely free my friends; you're going to make someone pick you up and pay for parking? You bastard.
MAKES YOU LESS MOBILE
Then there is the practicality of lugging around your bag. Arriving in an unfamiliar (or even familiar) place and being tailed by your bulky mass of possessions is no fun. Too much baggage may force you into an airport taxi (the worst kind of taxi) by making public transportation inaccessible to you (and some places taxis will charge you for luggage). You won't be running to make any trains or shuttles if your flight runs late either, so again, do yourself a favor and don't check a bag.