Here's one I've had in the back of my head for a while;
Batman and Joker are fighting, Joker dies in a freak accident (but it looks like Batman killed him), Harley Quinn witnesses the "murder" of her beloved Joker. She becomes blind with rage, A Red Lantern Ring seeks her out, she becomes a Red Lantern, she seeks revenge on Batman... and that's as far as I ever thought it out lol.
Another idea involves the Reds was;
Superman 2 movie (w/ Christopher Reeve) where he saved Lois Lane from dying in her car? How about he started flying around the world in rage (not knowing he was actually saving her by reversing time, lol). His rage consumes him, he gets ring, and becomes a Red. Lois Lane is saved but she had no idea what happened. Superman is now wreaking havoc on people. Somehow Lois Lane becomes a White Lantern and has to fight Supernan. The only way she can win the fight is to get the ring off him (but that would also kill Superman).