Numerous times. Known examples include Joan Redfern ("Human Nature"), Madame de Pompapour ("The Girl in the Fireplace"), and of course Rose Tyler and River Song. It has been suggested that the Doctor has possessed feelings for companions ranging from Jo Grant ("The Green Death") to Clara Oswald (several examples in Series 7 and "The Time of the Doctor"), but nothing clear-cut. For the record, on TV only two companions have ever said "I love you" to the Doctor: Rose in "Doomsday" and the TARDIS in "The Doctor's Wife", while several have indicated having feelings for him, including Sarah Jane Smith ("School Reunion"), Grace Holloway ("Doctor Who", the TV Movie), Martha Jones and Jack Harkness ("Utopia") and Clara ("The Time of the Doctor", but heavily hinted previously). In "The Aztecs" he even got (accidentally) engaged to a woman named Cameca.