Evolution on earth was a products of pure chance. Still, every living thing which has a personality to speak of knows the same basic emotional urges humans know. I don't think that is a freak accident, but a logical necessity. More clearly, I think it has to come down to the basic emotions we already know. That or you have something which doesn't really have a personality. And then you can just treat it like some sort of computer program. Like insects.
Fear, anger, lust for revenge, love, shame ectetera.. Sure different species will experience them differently, with different manifestations and weights and that can never fully be appreciated by any given species unless we get to transfer minds. But there is no emotional alternative to them, because those concepts already cover the whole scope.