One way for writing to go in unexpected directions is to violate people's assumptions about familiar storylines. Another is to break social norms.
For example, let's say we have a budding romance between characters who didn't hit it off right away--but the reader has reached the point where it's obvious the characters like one another. In this storyline, there will typically be a lot of friction and a lot of denial, which can work just fine. After all, in real life people strive to protect themselves in just that way. But sometimes a reader gets tired of watching this dance. Why not have one of the characters reach the breaking point and make a full-out, over-the-top play for the other? Or, on the other hand, why not bring in an alternate love interest for one of them--not someone the character pretends to love to evoke jealousy in the other, not someone the reader can tell is really shallow and will disappoint the main character eventually--but a real, viable challenger?
These are just examples off the top of my head. Of course any twists must fit the characters, plot and theme. There shouldn't be random twists just for the sake of fooling the reader. My point is to encourage writers to think: What could happen next? What else could happen next? What usually happens in this situation? Is there a different way to go? How would these characters really act? Is the reader too far ahead of the characters here--will the characters seem stupid if they go on like this much longer? Where's the fresh ground, the fresh angle?