I can't say they feel the same way humans do, but some animals do experience emotions. My sister has two dogs, and when someone pays attention to one of them, the other has to stick her nose in (literally) too. There are dogs that will do things just for spite when left alone. They know when a person is angry with them, and many know when they've done done something wrong. It can depend on what type of social interaction they experience.
I think some animals compete for your attention but I don't know if I would call it jealousy. It sure looks like it sometimes though. I have seen my friend's 2 cats push each other away while trying to get closest to her. And when I had two dogs they would not be happy if they thought one was getting more attention than the other.
Definitely, I've seen this with many animals: Rabbits cats parrots pigeons etc. This is especially true of cats. If you have a pet cat try petting some other cat in front of it, it'll be mad at you for some time.
Oh yes my pet bird would get so jealous and mad at me sometimes... It was really cute though and made me love him more.