I thought this warranted it's own discussion thread instead of clogging up others.

What is the appeal of Dick/Babs? Why do writers/fans like to see them together? What do the characters see in each other?

As a Dick/Kory fan I can see the appeal of them being together. Kory helped Dick open up his emotions and move away from the Batman's training which focused on making him cold, logical and emotionless. In turn Dick admires Kory because she is someone who survived a very harsh life yet still very warm, friendly and yet still ferocious as a fighter. Dick's relationship with Kory represents a life outside of Batman's shadow for him.

So in turn what is it that makes Dick/Babs tick?

If you want to argue why they don't work then this is the thread for it too.