I can give you a couple examples - there are many - it is what mainly contributes to the humor of the book (and film).
The first one that comes to mind is when Wesley has kidnapped Buttercup, beaten Fezzick and Inigo, and faces the Sicilian with the poison. You remember - they both drink - the Sicilian dies, and everyone is left to believe Wesley has outsmarted him and chosen the correct cup. It turns out he's been building up a tolerance to iocane powder for the past few years and both cups were poisoned. (Who saw THAT coming?!)
Next, it is ironic that Buttercup pushes Wesley down the big hill thinking he really is the Dread Pirate Roberts. Perhaps what is more ironic is that Buttercup is being such a spoiled princess at this time that you kind of wonder why Wesley is taking the time to rescue her at all.
It is ironic that Fezzick and Inigo fight Wesley in an attempt to KILL him (as per hire by the Sicilian) but end up needing him in the end... And they JOIN him because they are all so great at what they do. And then they LIKE him because clearly the three of them were actually meant to be together anyway.
The list goes on...
Well, for the most part - these are all examples of situational irony. Situational irony is when what the reader expects to happen does not happen; when what does happen is unexpected; or when the outcome of a seemingly common event goes astray from the norm.
This entire book is a satire. This means it is purposefully making fun of something cliche (in this case, fairy tales, hero stories, traditional love stories). This is not to say the entire thing is a big joke. It is simply to point out that instead of re-writing yet another fairy tale love story, William Goldman puts unexpected twists on every detail that would otherwise look like a cliche. I encourage you to look at the ironies in this story from a comparative perspective. Ask yourself, "If this was a typical romantic story or typical fairy tale, what would I expect to happen here?" When what you've seen before or expected to happen is different from what happens in The Princess Bride, boom, situational irony.
I'll give you another big one. How about the big "reunion scene" at the bottom of the hill where Wesley calls out "AS YOU WISH" while tumbling down? (Don't remember the chapter.) Goldman puts a note at the bottom saying he couldn't think of a suitable reunion scene that wasn't overdone, so he just skipped it. He even gives an address to write to if you want a copy of the scene that he later wrote. Well, in my high school worship of The Princess Bride you better believe I wrote to the address. I received (several weeks later mind you) a form letter apologizing that the reunion scene could not be distributed commercially or otherwise because of copyright issues. I was actually expecting an additional chapter to the book, sent to me for, at that time, thirty-seven cents.
*I'm now guessing there was no such scene ever written. The ironies never cease~!
Thanks for the points and evidences. But can somebody help me elaborate them further, like adding in insights and thoughts?