I looove reading angs so I'll just say what I enjoyed the most in the best stories I've read.
More than focusing on a to complicated plot, with too many plot twists, you should stress the attention on the emotions and feelings of the characters. It's still good to have twists though but it has to be something unexpected but don't just drop a bomb from nowhere, there has to be some hints, even subtle, throughout the story. Just like the user before me, I agree that fate plays an important role in an agst story.
Also a great vocabulary is the key. I'm not saying it has to be some kind of elevated language but the pain and sorrow in stories like this hit you the most when it's full of powerful forms of imagery.
I know it might be an obvious but just read lots of angst stories to get what I want to say. I recommend 'The person who once loved me' and loads of Kaistal angst stories on LJ.

omg im definitely an angst reader so yeah. Anyway, focus on the emotion of each character. You have to be detailed with everything. Dont put any useless unrelated angst emotion or feel or it will be gone. What makes me cry tho is when reality strikes, you know like when time, fate, destiny and reality is against their love for each other. Also, when the two really love each other that they would do anything for their love. Also when one of the main character is sick or maybe ill TT wow this is long, oh well, i love angst~~~

When you kill the other character and make his/her lover alive and make his/her life miserable. :)

when they love each other but have to pretend that they don't because of some circumstances??