Yes, as does the Twelfth Doctor, however the nature of this love is left deliberately ambiguous, leaving fans free to decide whether the love was platonic or otherwise. The fact the Doctor loves his companions as friends has been established on screen several times (see "A Good Man Goes to War" for example). But his feelings - whether platonic or otherwise is irrelevant - for some companions have been shown to be deeper than others. Prior examples to Clara have included Rose Tyler. A special case exists of course for family members, such as his granddaughter Susan, his wife River Song and his parents-in-law Amy Pond and Rory Williams.