I find these letters harder to write than the stories themselves!
I like plotty stories, strong characterization, and crazy AUs that remain true to the original. I like gen, het, and slash, but not negative portrayals of female characters simply because they are female. I don't like when animals are harmed (or children, unless it fits with canon :) ) I don't mind holiday stories, but I'm the atheist offspring of a Jew and a Catholic so I don't have strong feelings about them either. I have a not so secret secret rape- recovery story kink, but whatever you write I really, really prefer a comparatively happy ending!
Specifics, such as they are:
Bourne Legacy
I like that neither Aaron Cross nor Eric Byer are particularly morally upright, while still presumably believing they're doing the right thing. I really like the Sin Eater scene in the movie, and I'd like to see more of that interaction.
Left Hand of God
These books are a favorite of mine. I love the Bosco and Cale mentorship, but I also really enjoy the three boys' friendship. Anything true to the tone of the original will make me happy.
Rutshire Chronicles
I've been wanting Billy/ Rupert slash since before I knew what slash was! But I really like them as friends, too. And when I read Polo I kind of fell for Red Alderton, and I'd like to see things work out for him. Please note, you have my permission not to include all of these characters in your story, since the series takes place over this huge expanse of time. One or the other other would be just fine!
Political Animals
I loved TJ from the beginning, but I sort of fell for Doug there at the end, too. If you are squicked by incest, I will be totally happy with a brothers fic, maybe something where things fall apart for Doug and TJ has to step up and help him put his marriage back together? Or something where they reach a peace with their parents? I really like all the characters in this series but could only nominate four of them, so if you would like to include others that's fine!