Yes. The series unambiguously indicated (in "Doomsday" and "Journey's End", and with his actions in between those episodes) that the Doctor was in love with Rose Tyler. He later married River Song. And he has given hints of being strongly attracted to - and borderline obsessed with, per "The Bells of Saint John" - Clara Oswald.
Fans have also "shipped" the Doctor with other companions, most notably Romana (based on the real-life romance and later marriage of Tom Baker and Lalla Ward), Nyssa and Peri, but intentionally or otherwise, there is no on-screen evidence to be found.