In the 2008 episode "Forest of the Dead", River Song (a character whose timeline intersects with the Doctor in reverse order) says to the Doctor that she knows he would be able to open the TARDIS doors with a snap of his fingers. Although the Doctor dismisses this as impossible, at the conclusion of the episode, he opens and closes the doors by doing just that, eschewing the need for a key.
The Eleventh Doctor also does this at the end of "The Eleventh Hour", when revealing the newly regenerated TARDIS interior to Amy Pond; he then does it again in "Day of the Moon". In the 2011 episode, "The Doctor's Wife", he tries to open it by snapping his fingers, but the door is locked by the mysterious entity, House. This ability seems to be unique to the Doctor, though, as he said Time Lords cannot do that.