Taking a familiar trope and turning in on its ear can be a delightful practice ... but there reaches a point where the inversion itself becomes cliche. The first brooding "good-guy" vampire was probably a shocker; now you can't throw a stone in a bookstore without hitting one. Possibly literally. (I'm not wondering about the pale guy browsing the calendars, are you?) There have been so many stories where the knight comes to rescue the princess from the dragon - and the princess doesn't want to go, or is capable of taking care of herself, or ... that I'm no longer surprised by it. (I have yet to see a story where the prince comes to rescue the damsel and falls in love with the dragon, but I'm sure such stories exist. Hrm ... might be worth writing just for fun, actually.)
The best ever story I've seen on the dragon-knight-damsel triangle has to be from my childhood: Waiting For A White Knight, in Cricket magazine. But that just illustrates how long people have been flipping this one on its ear.
There are some trope inversions, however, that I feel haven't outlived their shelf life yet. One I'm particularly fond of works off the girl who disguises herself as a boy. Now, I'm willing to give this a pass as an overused trope in the first place, because it's a) practical and b) fairly common in history, as well. The only time I have a problem with this trope is when it's a major plot point or the reader is supposed to be surprised. (For the best treatment of this trope and all the asssociated cliches ever, read Terry Pratchett's Monstrous Regiment. One of his best.)
The inversion, of course, is a boy who disguises themselves as a girl for whatever reason ... and not to point to specific stories (because that would be a spoiler), I've done this and had a tremendous amount of fun with it. I also played with a different inversion in Just The Messenger: a character stares at the MC and threatens to expose her as a disguised girl. She bursts out laughing and points out that the various accoutrements of male attire are just more practical; she's not trying to hide.
Another trope I can't see skewered enough is a romance trope - the whole, wince-worthy I-can't-even-watch-the-screen tableau that occurs when one character has been keeping a big secret from another, the second character finds out, and then idiotically storms off without waiting for an explanation. Artificial tension and stupidity ahoy. I guess this is supposed to be sort of an object moral lesson: if you're dishonest, you pay for it. But nine times out of ten, it comes out forced.
I inverted this around in a story by having the MC withhold a secret. Someone else spills the beans for him while he and his SO are standing together. He rushes off without waiting for a reaction, just assuming she's not going to want anything else to do with him. He goes to see her later to make amends ... and finds out that she understands exactly why he was lying and doesn't particularly mind.
The prime problem with trope inversions, I think, is that they rely upon an element of surprise. Not the kind that pulls the rug out from under the reader, but the kind that elicits a reaction of, "Oh, wow! Really?" It's far easier for that surprise factor to wear off / become overused than it is for the original trope.
The Final Encounter, published by the good folks over at Aoife's Kiss, was my attempt to invert one more trope: the pulp fantasy / b-movie scene where the hero rushes up to the villain's tower to confront him. In this story, both characters ... decide to walk away, and their evolution from that denial of trope is the story. Unfortunately, when attempting to sell it, I got a few rejections that criticized the use of tropes. This, to me, missed the point, but it's also a relevant complaint, and illustrates another danger with breaking tropes: you have to get a jaded reader who's seen the dragon-knight-damsel a hundred times to read on far enough to enjoy the inversion.
Of course, there are those of us who take this as a thrown gauntlet ...