Most modern idle animations are boringly realistic. Your characters do what you would do -- like stretch or scratch themselves. It's better when these animations reinforce the idea that your avatar is alive and part of the gaming experience with you. Whether it's in-jokes or breaking the fourth wall by blatantly asking you what the hell you're waiting for.
And then there's the rare type of idle animation that can actually cause a Game Over. As in...
Yes, it is once again tail time, thanks to Limited Run Games.
Tormeted Souls II has its apparent flaws, but it also happens to be a great horror game and throwback title to the classic survival horror days.
Overture is the prequel/DLC to one of the best Soulslikes, 2023's retelling of the Pinocchio story, Lies of P.
Conker's Bad Fur Day definitely has some of the best idle animations ever.
LOL get game over with Sonic. I didn't know he could talk in those days.