Hi, guys!
I’ve been watching a lot of go lectures and commented professional games, and there’s one particular question that surfaced for me that I still haven’t found an answer to:
When there’s a ladder, why do people check who has a ladder-breaker in the distance, if ladders never get played out?
It, kind of, confuses me. 
To determine who can play what. The ladders never get played out because they’re predictable. If there’s no ladder-breaker, the player trapped in the ladder cannot play it out. If there is, the player on the outside cannot play it out.
Here’s a very contrived example. Note that both players would typically be able to read out what would happen, so you’ll (almost) never see this in a higher level game (Lee Sedol’s broken ladder game is one notable exception) because the players will make their followup moves based on what the situation on the board is.
Click Variations 1 and 2 to see how this may progress.
ladder-example.sgf
Also, when your stone (or stones) is already caught in a ledder playing a clever ladder breaker kind of gives you at least something out of the situation. Your opponent then has to decide wheter to respond to the stone you played (the ladder breaking one) and thus let you save the original stone(s) or capture the laddered stone(s) and thus basically giving you a free move around the ladder breaking stone.
Hope I managed to made it at least a little understandable 
Hi again!
I do understand the concepts, it’s just that as @pbgarden said, they’re predictable, thus I never expect to see them be played out. Both players know that there is, or there is going to be a ladder there, and they don’t even bother.
I’ve heard or read about that before, somewhere; I’ll look it up.
The doubt that I had is because of people looking at, literally, the other side of the board for a stone already in place over there, but… it’s just really silly, since no one is going to play that thing from corner to corner. So… yeah.
But, close by, I totally get this. I normally always play ladder-breakers close by, though I had never analyzed it deeper like that. I really liked the whole explanation, @Adam3141.
Thank you very much guys! 
It helps far away just as it does close by. These stones determine if a ladder will work or not, and thus who can play. As in my example, without a ladder breaker, white can’t play at 1 immediately. There are a lot of subtle but important strategic aspects to this based on black being able to hane those white stones without having to worry about the cut. If the ladder breaker was there, this could possibly be a mistake (all depending on the whole board picture).
@amusicianrs I think one point you are missing is that in a game you usually check the ladder-breaker BEFORE the ladder even exists.
An example from one of my current games:
At move 17, black doesn’t play F15, both players know that the ladder is not working. The key here is that white had ALREADY read the ladder-breaker at move 10, before playing E15 or even D16. Without the ladder breaker white would not have played D16 in the first place and there would be no ladder.
As a reference, the initial sequence is known as the “Magic Sword of Muramasa”:
http://senseis.xmp.net/?MagicSword
[Update] Another fresh example (move 27):
That ladder is tricky, but anyway the point is that black had to consider the ladder-breaker before deciding to play E17.