Reboot was never THAT bad.  This looks like a Sims machinima.

the main thing to any kind of animation to make it look realistic is to avoid robotic movements and to be aware of the weight and dynamics of the character. to a certain extent, this is easier in hand-drawn 2d animation, because in 3d it can be too easy to say, just move an arm upward without giving any regard to the res of the body.

if you look at the 2d disney films, they over-exaggerate the weight distribution as characters move to make them very dynamic and fluid. it's not always how a real person would move, but as in theater, the exaggeration helps to get the point across.

in this video, you'll notice that one of the reasons people look so stiff is that they're only moving whatever relevant body parts. when the doctor moves his arm up, he's just moving his arm, when in reality, he should also probably be arching his back somewhat, bending his knees a little and using the other arm for a little bit of balance.

if you're animating a horse for example, if the legs are just going through the run cycle of bend, extend, bend, back, the horse isn't going to look realistic at all, because as a real horse runs, it uses its entire body-- its spine flexes, its head moves up and down and its haunches flex.

so basically, the key is to be aware of the movement of the entire body, not just the part you're moving. i've got this gigantic book called Disney Animation the Illustion of Life that i've had since i was a kid. when i was a kid, I really really wanted to be an animator, but at the time, the only thing going was 2d animation and i realized i didn't have the patience for it. but if you can find it, it's an incredibly wonderful and thorough book on animation. It was written in 1984 by Ollie Johnston, one of the first Disney animators, so it's an invaluable wealth of info on the history of animation and techniques.