Persuasion is my favourite Austen. Also the one I'm most likely to go back to. Now really in the mood to reread some of Heyer's Regency Romances, which I haven't looked at in years! Totally agree about old friends -- a short story by Suzy McKee Charnas has been a beloved companion since I turned 18.I reread books that have made it to my "comfort reading" list. Books like Anne of Green Gables, the Courtyard of the Others series, some of Georgette Heyer's Regency Romances, some of Agatha Christie's mysteries, Jane Austen's Persuasion etc.
These get pulled up and read on days when I really have no more mental energy left. It's like spending time with old friends who come to life on the page.
For more recent books, I reread Becky Chambers' The Long Way to a Small, Angry Planet, and A Closed and Common Orbit. Both lived up to, and exceeded, their first readings. A few romances have been retried to good effect, too: some of Gerri Hill's work, and Melissa Brayden's.