Oh wow, interesting topic! That's one thing I really like that they added in X and Y, especially with the games becoming more 3D. My favourite fainting animation in there is definitely Haunter's "NOOOOOOOO" pose and Mr. Mime's spinning facepalm. It's also really amusing to knock out a whole bunch of Pokemon at once in a horde battle. Probably since their animations don't happen at the same time; they're staggered a bit to make it look more realistic.
I remember that before X and Y, I was really missing the fainting animations from earlier games, especially the stadium ones. I really liked the Misdreavus one where it stretches out then disappears, leaving only its necklace which breaks apart and the beads scatter on the floor. And Kadabra's, which had it sink into a sitting position and throw its spoon in the air, and then the spoon falls on its head and it acts all dizzy. And also Togepi's, where it turned around and ran back to its trainer before falling forward. ("Mommy!") The eye-popping Electrode originated from there too.
And then there was the comment on other animations in the console games, like ones where the Pokemon got hit. That I do have to agree on. I remember in Colosseum, whenever Medicham got hit, it fell as usual, but then got up and did a graceful little flip, as if it was some sort of acrobat. Way to make one of my favourite Pokemon that much more awesome.