In principle, yes, this can happen. In practice, it is very rare. Speaking personally, in years of travelling, I have only ever once had someone try to walk off with my own luggage … and that was on a suburban bus on my way home. (I never did figure out if they were an opportunistic but incompetent thief, or just someone a bit drunk and confused.)
There are a couple of anti-theft measures that do appear sometimes. In some airports, there are baggage checks – people are stopped on their way out and asked to show the claim tickets for their bags. (You are given these with your boarding pass.). In some circumstances, you may also be stopped for customs inspection (when arriving from international flights), which would be a problem if your bags clearly did not belong to you.
There are other factors that help mean theft is mostly quite low-probability. The first is that most luggage isn’t really that valuable. It’s worth something to the owner, but to most other people it’s fifteen kilos of laundry, and 50:50 chance it’s not even clean laundry. If people are transporting valuables, they usually do so in their hand luggage – you won’t find many laptops or cameras in suitcases. You might get lucky… but you probably wouldn’t.
The second is that most baggage claim areas are not open to the public; everyone standing around is another passenger (or airport staff). Not that everyone who takes a plane is scrupulously honest – but it’s a lot of effort to go to to have a chance of stealing a suitcase!
Thirdly, most of the time, the reason there is a scrum at baggage collection is because all the passengers have arrived before the bags do. Everyone is looking out for their own bag and trying to get to it first. In these circumstances, you’d have to be a pretty bold thief to try and pick up a bag without the owner spotting and confronting you.
People picking up the wrong bag does happen, however, but mostly due to innocent confusion – especially if you all went to the same shop and bought the same range of luggage. The best approach here to make sure no-one gets your bag by accident is to make sure it is visibly yours – a popular approach is to put a brightly coloured address label on it, for example (always a good idea anyway in case it gets accidentally put on a plane to the wrong destination), or something like tying a coloured shoelace/ribbon around the handle.
So while your luggage being taken by someone else intentionally is not a very high risk, you can mitigate the chance of it happening by accident quite easily – just make sure your luggage is distinctive enough that someone else with the same suitcase won’t think “oh, that’s mine”.
Lastly, as I mentioned, you can carry high-value items in your hand luggage while putting your clothes, etc in the hold luggage. I think everyone would recommend this if possible – if your bag does get lost, much easier to deal with buying some new shirts than a new laptop.