I think that realism is a sort of extra credit add-on. It's nice if you can throw some in there, but it shouldn't constrain you as long as the animation still looks good anyway.
To clarify, I am talking more about physics than about powers and effects.
To illustrate my point I have some volunteers who are willing to perform for you.
Subject A

Subject A is unrealistic. He jumps higher than it is physically possible for a human to jump. Is that what makes this a bad piece of animation, or is it just the lack of easing?
Subject B

Subject B does not break any laws of physics. He is fully constrained by gravity, momentum, and reaction. Despite this, he could be considered unrealistic. Just you try getting down on one leg with the knee bent more than 90 degrees and the other knee stretched out in front of you, and then push yourself up fast enough to flip over backwards. It's not just you being unfit, it is simply as impossible to do as it is for someone to jump as high as Subject A. Is this still a good animation?
Subject C

Subject C is quite realistic. With a bit of practice, training and the right apparatus someone could actually do this. It's a decent animation, but is it only so because of the fact that it is possible?
Subject D

Subject D is perfectly realistic. Anyone can do this. You've seen people doing it in the street. It's also by far, in my opinion, the best animation I've ever made. Does this fact in itself mean that the viewer is going to sit there for an hour staring in awe at my walk?
Note: I didn't make these animations with this thread in mind. Subject C is not as realistic as maybe I would have made him if I had, but it would have been quite unfair to bring one of my older, worse, animations in to support the realistic side when this one would just aout do.