In Doctor Who, Time Lords such as the Doctor have two hearts, which got me wondering if they need both to survive or if the second heart is so that if one stops working they can still survive (kind of like a backup generator). And if they can survive without one heart working, will it be harmful to them or reduce their physical abilities at all, or can they go on with just the one with no ill effects, for at least a limited time?
We see the Doctor survive having one heart stopped in The Shakespeare Code (Martha restarts it shortly after)
We see another in The Power of Three
RESEARCHER: Hospitals are logging a global surge in heart failures. Cardiac arrests.
DOCTOR: That's it. Oh! Oh! Oh! Only one heart. Other one's not working.
It seems this isn't a good state for Time Lords, however. As we see in both instances, The Doctor suffers with only one working
AMY: Okay, how long are you going to last with only one heart?
DOCTOR: Not much longer. I need to locate the wormhole portal.
Time Lords (or at least properly educated ones, so perhaps not the Doctor) can voluntarily stop both their hearts and be fine. Romana demonstrates this in "Destiny of the Daleks."
DOCTOR: Romana. Ha ha! I thought you were dead.
ROMANA: Well, the only way to escape the Daleks was to feign death. It's lucky they didn't know I was a Gallifreyan.
DOCTOR: Good girl.
ROMANA: Yes, they taught me at school how to stop my hearts.
TYSSAN: Hearts? How many have you got?
ROMANA: One for casual, one for best.
When both her hearts are stopped, she feigns death but is very much alive. So exertion may be impossible without at least one ticker running, but it is definitely possible to be alive with neither heart pumping at all.
Moreover, in the third Doctor Who Serial ("The Edge of Destruction"/"Beyond the Sun"/"In the Ship" are among it's names), the First Doctor is heard to have only one heart. Some fans and extended universe media ran with the idea that Time Lords only grew a second heart when they regenerated for the first time. So again we have an instance of a Time Lord functioning with less than two operational hearts.
This exact scenario occurs in the Eleventh Doctor story "The Power of Three" (Series 7, Episode 4). In that episode, a bunch of black cubes from space (cosmic cubes, if you will) mysteriously arrive on Earth. Their purpose is initially unknown, and the people of Earth eventually forget them, using them as paperweights and such. After a year on Earth, the cubes begin to actually do something, scanning people, glowing, etc. They start sending people into cardiac arrest, including the Doctor. Only one of his hearts fails, though. It is a very painful process for him, as he states that only one heart can keep him alive:
I can't do it! I need both hearts!
His companion Amy uses a defibrillator to restart his second heart, as seen in this scene (from 0:59 - 1:10): Doctor Who - The Power of Three - Funny moments