The immediate answer and easy is, of course, Dr. John Watson. I relate to his intelligence: high, but not out of the ordinary, and often frustratingly inadequate when placed beside brilliance. I relate to his honest, hardworking nature. I admire and try to emulate his loyalty and courage. And, naturally, we're both in the healing professions and friends with people who habitually put themselves in the way of danger. Every time I read the Holmes stories, I see myself in Watson's exasperated love for his rather reckless friend.
Along those lines, I relate to Jonathan (of David and Jonathan) as well.
Among the classics, I relate to Anne Elliot from Austen's Persuasion. I'm loud where she is quiet, but despite this difference we're very similar: too easily swayed by others' opinions, always struggling to do the right thing, and lovers of books and good music.
But really, for sheer similarity, I identify with Lusa Landowski from Barbara Kingsolver's novel Prodigal Summer. An entomologist (specializing in moths, no less!) turned farmwife, Lusa and I have the same inquisitive mind, love of reading, lazy streak, and ineptitude at house-wifey skills. We have the same temper, stubborness, and sense of marriage to the land we belong to.