At first glance, the story of a grey-haired eccentric inventor and his teenaged sidekick makes Rick and Morty look like a Back to the Future parody. A few episodes into the multiverse misadventures, moral ambiguity, and wacky science makes it feel like the Brian and Stewie episodes of Family Guy.
But after two and a half seasons, Rick is starting to act more and more like the Doctor.
Strip away the crude humor from one and the British charm from the other, and what you are left with is a godlike figure who travels around looking for excitement and along the way. He saves lives, makes the hard choices nobody else wants to, and messes with the lives of his companions.
Rick and Morty has no clear reference to The Doctor. This suggests that any parallels between everyone's favourite murderous, space travelling, amoral super-scientist and Rick Sanchez are a complete coincidence.
One character is a benevolent, professor type and the other genius, misanthrope yet they both turned out to be arrogant, absent-minded scientists, just out for a good time despite their HUGE body counts.