This is challenging for me, because I never know what sane people define as "cute". Or at least that's what I've been accused of after going on about what adorable faces snakes have. I still don't believe I'm wrong.
Anyway, here's the California Condor. Apparently critically endangered, but has an oddly shaped beak and very unusual, spiky feathers.
(Although this is another web page where I think that most of the animals here are cute. The frog, the snake, the sloth, and the okapi pictured on this link especially.)