Tom Baker. He had 176 episodes as the Fourth Doctor (from "Robot"-"Logopolis", as well as cameos in "Planet of the Spiders", "Castrovalva", "The Five Doctors" [footage from "Shada"], and "The Day of the Doctor" [playing 'the Curator', who may or may not be another version of the Fourth Doctor]). He also had the most TV STORIES, with 41 (in his era), although David Tenant comes a close second with an era consisting of 36 stories.
If you count every medium, then Paul McGann's Eighth Doctor beats him, but only his single TV-Story, "Doctor Who", his exclusive-to-iPlayer regeneration story, and the Big Finish stories required an actor. Books ("The Dying Days" (Virgin New Adventures novel), The 'Eighth Doctor Adventures' Novels (EDAs), etc.), comics and short stories merely used his likeness. The Tenth Doctor also comes in Second Place by this count.