Some animals definitely feel emotions, emotion are the basic workings of the brain, variations in neurotransmitters used to tag experiences and alter behavior. If it has a brain and is capable of learning if feels some emotions, even if only pleasure or discomfort.  Not every animal is going feel them all, and animal covers a very wide group, a sponge is an animal and almost certainly feels no emotions as it lacks a brain, but exactly which emotion each animal experiences is impossible to say, we can't even say for certain every human experiences every emotion.
 
As for specific emotions as far as we can tell every emotion humans experience is represented somewhere in the animal kingdom. It is extremely unlikely emotions arrose ex nihilo in humans given the similarities in behavior between humans and other animals, especially primates. [Bonobo'][1]s for instance even show similar emotional managements skills to humans. 

A consensus is a tricky term emotion in animals has been a taboo subject for a long time, and there are still pockets that assume animals experience no emotions and operate on pure logic, but this view has never withstood scrutiny.
  [1]: http://www.pnas.org/content/110/45/18121