In Gone with the Wind, Scarlett marries a random man to make Ashley jealous. It doesn't work, because Ashley was never interested in her in the first place and was actually already in love with someone else.
In Sky High (2005), Layla started a fake relationship with Jerk with a Heart of Gold Warren Peace in order to annoy Will. Warren, who thought Will was a prick, was happy to oblige, but ended up getting sick of Layla clinging to him and talking Will into asking her out.
Warren: Dude, you are so stupid. She's totally into you. Will: Not after tonight. I wouldn't be surprised if Layla or any of the other guys never talked to me again. Warren: You must've been a real jerk, because no matter what I do, I can't get them to stop talking to me.
In The Thomas Crown Affair (1999), Thomas the Gentleman Thief likes Catherine the Hot Detective, but he doesn't know if he can trust her. So, he lets photos leak of him dating a supermodel to see if he gets a rise out of Catherine. It does. They hook up.
The main characters of Drive Me Crazy form a fake relationship to make the people who dumped them jealous. Predictably, by the end of the film they can both have their respective love interest, but they no longer want them and have fallen for each other.
The female protagonist of Two Can Play That Game institutes her "Ten Day Plan" involving this trope to bring her man "back in line". Meanwhile, her man's best friend urges him to do the same. Naturally, both plans backfire, and they have to have an honest conversation in order to get back together.
In Sgt Bilko, After Bilko ditches his fiancee at the altar for the second time, she gives him one chance to marry her within a month, after which she's done with him. Deciding to mess with Bilko in every way, Major Thorne starts hitting on her and takes her out a few times. Discovering this, Bilko has one of his soldiers dress as a woman and go to the same restaurant where Thorne and his fiancee are at. Naturally, she isn't stupid and recognizes it for what it is (not to mention only a blind man would think that the soldier was really a woman) and reveals that she was doing the exact same thing to Thorne.
In Scott Pilgrim vs. The World, after Scott dumps Knives for Ramona, Knives puts blue highlights into her hair (since Ramona subscribes to the You Gotta Have Blue Hair philosophy), starts dressing more like Ramona, and begins to date Young Neil, all to be close to Scott and make him jealous. It doesn't work, although Scott does freak out when Todd punches Knives so hard her highlights fall off. In the end, though, she pulls an I Just Want My Beloved to Be Happy, so that Scott can be with Ramona (in an alternate scene, he stays with Knives).