Doctor Who is a long running British science-fiction television series. It is the parent show of bisexual sci-fi Torchwood.
Doctor Who introduced the omnisexual/bisexual Captain Jack Harkness as a recurring character in 2005. Jack later became the star of Torchwood. In Jack's home era, the 51st century, people are generally very open about sexual orientation, as dating alien species is not uncommon ("The Doctor Dances"). Presumably River Song ("Silence in the Library") is also omnisexual, as we know she has at least dated robots.
Mickey Smith meets himself from a parallel universe. The alternate Mickey (Ricky) is in a relationship with a man, although Mickey himself is heterosexual identified.
The show's protagonist, The Doctor has generally asexual attitudes towards his friends, though he has been kissed by both women and men ("Parting of the Ways"). There is also some speculation within fandom as to the nature of his relationship with adversary, The Master. In "The Time of the Doctor", the Doctor himself mentions creating an android boyfriend.
William Shakespeare appears in "The Shakespeare Code". He flirts with both Martha Jones, and The Doctor. The Doctor comments on Shakespeare's bisexuality, referencing the theory that some of Shakespeare's poems convey his bisexuality.