Most of my fictional characters like to read. I don't go into a lot of detail about what's in their TBR (product placement doesn't interest me) but personally knowing what they prefer to read is part of the characterization process for me.
Alexandra Keller is a big fan of Linda Howard because she likes her no-pushover heroines. Jema Shaw adores Jane Austen for the affection she shows for families in her stories. Even Samantha Brown, my homicide detective who sees the worst of reality, finds refuge and spiritual renewal by reading beautiful old poetry.
I've never been tempted to portray one of my characters as a fan of my books, oddly enough. I think that would be as ridiculous as giving myself a quote. Or maybe I've never recovered from reading a fiction book by an author who inserted their real self into the story to serve as a character. Not sure.
Some of my characters enjoy books that I don't particularly care for. Nick from Night Lost has a nice collection of nonfic books at her farm; they're all about motorcycles and baseball and I'm every one of them would put me to sleep in under a minute. Duncan Reever seems to like every Fred Saberhagen and Robert Silverberg novel that's ever ticked me off and/or given me a monster headache, especially The Veils of Azlaroc and The Man in the Maze.
Right now I'm mentally inspecting my new protagonist's bookshelves to see exactly what she's been reading. I can envision a tidy row of novels by Dick Francis, Val McDermid and Jeffrey Archer, but I think she's got a small stack of books tucked out of sight behind them. When I figure out what my protag would want hide from view, I'll know a little more about her.
What is one of your characters reading right now? If you don't know, what do you think they'd enjoy reading, and why?