Yes, there are several things outside programming that can be said to be like monads. No, none of them will help you understand monads. Please read Abstraction, intuition, and the “monad tutorial fallacy”:
Joe Haskeller is trying to learn about monads. After struggling to understand them for a week, looking at examples, writing code, reading things other people have written, he finally has an “aha!” moment: everything is suddenly clear, and Joe Understands Monads! What has really happened, of course, is that Joe’s brain has fit all the details together into a higher-level abstraction, a metaphor which Joe can use to get an intuitive grasp of monads; let us suppose that Joe’s metaphor is that Monads are Like Burritos. Here is where Joe badly misinterprets his own thought process: “Of course!” Joe thinks. “It’s all so simple now. The key to understanding monads is that they are Like Burritos. If only I had thought of this before!” The problem, of course, is that if Joe HAD thought of this before, it wouldn’t have helped: the week of struggling through details was a necessary and integral part of forming Joe’s Burrito intuition, not a sad consequence of his failure to hit upon the idea sooner.
But now Joe goes and writes a monad tutorial called “Monads are Burritos,” under the well-intentioned but mistaken assumption that if other people read his magical insight, learning about monads will be a snap for them. “Monads are easy,” Joe writes. “Think of them as burritos.” Joe hides all the actual details about types and such because those are scary, and people will learn better if they can avoid all that difficult and confusing stuff. Of course, exactly the opposite is true, and all Joe has done is make it harder for people to learn about monads, because now they have to spend a week thinking that monads are burritos and getting utterly confused, and then a week trying to forget about the burrito analogy, before they can actually get down to the business of learning about monads.
As I said in another answer long ago, sigfpe’s article You Could Have Invented Monads! (And Maybe You Already Have.), as well as Philip Wadler’s original paper Monads for functional programming, are both excellent introductions (which give not analogies but lots of examples), but beyond that you just keep coding, and eventually it will all seem trivial.
[Not a real answer: One place monads exist outside all programming, of course, is in mathematics. As this hilarious post points out, “a monad is a monoid in the category of endofunctors, what’s the problem?” :-)]
Edit: The questioner seems to have interpreted this answer as condescending, saying something like “Monads are so complicated they are beyond analogy”. In fact, nothing of the sort was intended, and it’s monad-analogies that often appear condescending. Maybe I should restate my point as “You don’t have to understand monads“. You use particular monads because they’re useful — you use the Maybe monad when you need Maybe types, you use the IO monad when you need to do IO, similarly other examples, and apparently in C#, you use the Nullable<> pattern, LINQ and query comprehensions, etc. Now, the insight that there’s a single general abstraction underlying all these structures, which we call a monad, is not necessary to understand or use the specific monads. It is something that can come as an afterthought, after you’ve seen more than one example and recognise a pattern: learning proceeds from the concrete to the abstract. Directly explaining the abstraction, by appealing to analogies of the abstraction itself, does not usually help a learner grasp what it’s an abstraction of.