Doctor Who doesn't tend to cast many non-white actors, especially in the role of companion, but Indian Freida Pinto would excel as the Doctor's best friend. Originally only a model, Pinto got into acting on the back of Slumdog Millionaire, and received multiple award nominations for her role as Latika. Director Danny Boyle claimed that he knew she was right for the part just from her audition tape; she has an effortlessness in front of camera, and can play both shy and commanding characters. If she were to appear in Doctor Who though, it would certainly make for an interesting relationship with the Doctor.
7. Lara Pulver
Another star that Steven Moffat has worked with on Sherlock, Lara Pulver is an actress who was rumoured to have been cast as the Twelfth Doctor. Again, she'd provide a different dynamic to Doctor Who though, as she's much more a River-type character than say Amy or Rose. Though she's excels at playing love interests with rivalries - and not just as Irene Adler, but in Skins: Fire too - it would be interesting to see her acting opposite Capaldi, showing more of the humour she's capable of. It would be surprising if she actually was cast as a companion, but surely she's going to appear in Doctor Who at some point or another?