"They don't check that it's yours at the door"? According to the mouse-over text for this XKCD comic strip:
That's scary. I wonder what are the chances of getting your luggage stolen (from the conveyor belt, not lost by the airways company).
Many common practices in airports won't prevent a passenger from committing the theft, however they would be very good at identifying the thief afterwards. Airports tend to have full coverage of high quality video monitoring, they can backtrace a person in video to their plane, and they are rather sure about the identity of passengers on every airplane.
In essence, you'd leave behind video evidence that proves the crime and also your ID and address - there is a very high risk of getting caught that would generally outweigh the benefit of getting a suitcase full of clothing and my toothbrush, and if someone would intend to do it repeatedly, then it's not realistic to remain undetected.
It depends on where you are and how you're travelling. If you need to pass through customs then the baggage collection area is typically closed to all but travellers, so requires forethought and an outlay of a flight to gain access.
However in some circumstances, i.e. domestic flights, definitely in Australia and the U.S. amongst others, the statement is absolutely true. You can walk into baggage collection from outside and just pick up a bag and walk off.
The chances of getting something worthwhile instead of just some dirty clothes versus the chances of getting caught is presumably low enough to deter thieves, otherwise we'd see many more cases of it when it's possible.
Yes they don't check it. Why there isn't more theft? This has been discussed on Metafilter and I think this comment sums it up:
The simple answer is that there's no way to know that the owner of the bag you're taking isn't standing right next to you. Throw in all the security measures nearby, and any thinking thief is going to prefer shoplifting or purse-snatching.
It's not that scary actually. To be in the arrival hall, you usually need to be traveller or find some way to go around airport security. The rightful owner of the bag is probably around too, as are many other people, and law enforcement personnel. And then you often have to walk through customs where you could be stopped or interrogated, without even knowing if there is something to declare in the bag. Even without anybody actively monitoring, showing up regularly and not looking the part could increase the risk of being caught.
Of course, there are some places (e.g. domestic terminals in the US) where some of this does not hold and a fellow traveller could also just grab a bag everywhere. But even if you are inclined to steal a bag, you need to be lucky and to have local contacts to offload anything worth your while. And as others also mentioned, some airports do occasionally check luggage tags at the exit. All in all, not the most welcoming environment for a criminal.
The thing is also that before ending on the conveyer belt, your bags spent hours in airport facilities to which hundreds of people have access. Even if you would expect some level of vetting and monitoring, the sheer volume of luggage and number of airports in the world means security often won't be very good. So employees can and do steal bags and at some airport theft can become a serious issue (at least temporarily until the authorities crack down on it). In comparison, the conveyer belt isn't such a huge issue.
Finally, there are countries (OK, Switzerland) where newspapers or vegetables are simply left on a table or similar device on the streets and people are expected to leave money behind if they take one. It won't work everywhere or in any context but generally speaking we do rely to a larger extent than we might believe on social norms and plain old honesty rather than exclusively on incentives and technical enforcement measures.
For what it's worth, there are some airports where they do check. In particular, for domestic flights in Japan, they often (but not always) have people at the exit who verify that you've got a bag tag from check-in that matches the tag on the baggage you're taking out. Air Do:
Upon arrival of destination, confirm your "baggage claim tag" by yourself. Please make sure not to pick up baggage of another person by mistake. Please hand the baggage claim tag to the clerk at the Arrivals exit gate.
Anyway, the easiest precaution to guard against this is to have wacky-colored baggage, instead of those ubiquitous black bags. My family's usual travel bag is a lovely neon green number, which not only makes it easy to spot on the conveyor belt, but also makes it difficult for a thief to credibly pull off the "I'm sorry, I thought that was mine" routine.
In some airports, the luggage tag on your luggage is checked against the copy typically affixed to your ticket, by airport personnel. This is exceptional, however.
So, although the chances of random passengers taking other people's luggage intentionally are small, it's definitely possible in many airports.
If I would have nefarious intentions, I would fly with a nondescript, common, piece of luggage, stuffed with cheap second hand clothing, then pick another, similar looking bag, from the conveyor belt upon arrival. This way, I could apologise for 'mistakingly' picking the wrong bag, if caught.
That said, if you're packing anything in your checked in luggage that you can't lose and is not insured (and many things aren't when packed in checked in luggage), you probably should pack differently.
Thieves aren't mindless stealing zombies. They are probably a lot like you and me, mostly rational, just jerks.
So to understand why a baggage claim is safe, you have to think like a thief. Assuming you're not into burglary, the recipe is simple:
This is what you do at a beach, at a concert, at a park, bus terminal, etc. This is how you pickpocket someone, how you mug someone, and the core formula for a myriad of scams travelers fall for.
The key element of all this is that you must pick your target carefully. An airport is the worst place in the world to do this, since you never know whose stuff you're stealing. Worse, whoever it is they are (generally) sober, and probably aren't very distracted by anything other than finding the same bag you're trying to steal.
In the end the problem with airports is that you can't see people when they drop off their bag. Even if you were somehow crafty enough to post people on the other end of the flights, which flight would it be? Given the amount of planning required, you'd be better off breaking into a house.
For a German like me, most of the time they did not check my luggage when I left the German airport.
They did not check the tags in the US a couple of years ago, either.
However, they might inspect "your" belongings closer for customs, asking what you are bringing into the country and might notice when the tags show names other than yours, which happened to me in the US and Australia.
I cannot tell whether they really compared the tags, though, but in the end, that same xkcd "fact" is the same thought I've always had when leaving the aircraft.
This is why I always hurry to pick up my luggage.
It once happened to me in Germany that someone took my stuff, but at least they were honest and probably wanted to get theirs back (there was exactly one trolley left on the conveyor belt; wasn't mine), so few days after, airport staff brought me mine right to my home.
Regarding customs, if you go to customs and ask if you are allowed to bring (some legal stuff, e.g. a cake), they usually think you're honest enough to let you through.
The answer is yes. I know a person who took someone else's bag by mistake (they looked almost the same). He only realized when he arrived home (3 hours later) and opened the suitcase. No one asked anything, the owner didn't notice him taking the suitcase at the belt, and no questions were asked on exit. He had to return later to bring is the case and take his own. Of course this is a particular situations and it's possible that checks change from airport airport.
Having this said, I don't think it's a big problem else aiports would control it more. There are several aspects that dissuade luggage being stolen:
I don't think the risk is null but it's probably neglectable.