For me, this is an easy question. I believe that animals have feelings and other states of consciousness, but neither I, nor anyone else, has been able to prove it. We can't even prove that other people are conscious, much less other animals. In the case of other people, though, we at least can have a little confidence since all people have brains with the same basic configurations. But as soon as we turn to other species and start asking questions about feelings, and consciousness in general, we are in risky territory because the hardware is different.
When a rat is in danger, it does things that many other animals do. That is, it either freezes, runs away or fights back. People pretty much do the same things. Some scientists say that because a rat and a person act the same in similar situations, they have the same kinds of subjective experiences. I don't think we can really say this.
There are two aspects of brain hardware that make it difficult for us to generalize from our personal subjective experiences to the experiences of other animals. One is the fact that the circuits most often associated with human consciousness involve the lateral prefrontal cortex (via its role in working memory and executive control functions). This broad zone is much more highly developed in people than in other primates, and whether it exists at all in non-primates is questionable. So certainly for those aspects of consciousness that depend on the prefrontal cortex, including aspects that allow us to know who we are and to make plans and decisions, there is reason to believe that even other primates might be different than people. The other aspect of the brain that differs dramatically is that humans have natural language. Because so much of human experience is tied up with language, consciousness is often said to depend on language. If so, then most other animals are ruled out of the consciousness game. But even if consciousness doesn't depend on language, language certainly changes consciousness so that whatever consciousness another animal has it is likely to differ from most of our states of consciousness.
For these reasons, I think it is hard to know what consciousness might be like in another animal. If we can't measure it (because it is internal and subjective) and can't use our own experience to frame questions about it (because the hardware that makes it possible is different), it become difficult to study.
Most of what I have said applies mainly to the content of conscious experience. But there is another aspect of consciousness that is less problematic scientifically. It is possible to study the processes that make consciousness possible even if we can't study the content of consciousness in other animals. This is exactly what is done in studies of working memory in non-human primates. One approach by that has had some success in the area of conscious content in non-human primates has focused on a limited kind of consciousness, visual awareness. But this approach, by Koch and Crick, mainly gets at the neural correlates of consciousness rather than the causal mechanisms. The correlates and the mechanisms may be the same, but they may not. Interestingly, this approach also emphasizes the importance of prefrontal cortex in making visual awareness possible.
So what about feelings? My view is that a feeling is what happens when an emotion system, like the fear system, is active in a brain that can be aware of its own activities. That is, what we call "fear" is the mental state that we are in when the activity of the defense system of the brain (or the consequences of its activity, such as bodily responses) is what is occupying working memory. Viewed this way, feelings are strongly tied to those areas of the cortex that are fairly unique to primates and especially well developed in people. When you add natural language to the brain, in addition to getting fairly basic feelings you also get fine gradations due to the ability to use words and grammar to discriminate and categorize states and to attribute them not just to ourselves but to others.
There are other views about feelings. Damasio argues that feelings are due to more primitive activity in body sensing areas of the cortex and brainstem. Pankseep has a similar view, though he focuses more on the brainstem. Because this network has not changed much in the course of human evolution, it could therefore be involved in feelings that are shared across species. I don't object to this on theoretical grounds, but I don't think it can be proven because feelings can't be measured in other animals. Pankseep argues that if it looks like fear in rats and people, it probably feels like fear in both species. But how do you know that rats and people feel the same when they behave the same? A cockroach will escape from danger--does it, too, feel fear as it runs away? I don't think behavioral similarity is sufficient grounds for proving experiential similarity. Neural similarity helps—rats and people have similar brainstems, and a roach doesn't even have a brain. But is the brainstem responsible for feelings? Even if it were proven in people, how would you prove it in a rat?
So now we're back where we started. I think rats and other mammals, and maybe even roaches (who knows?), have feelings. But I don't know how to prove it. And because I have reason to think that their feelings might be different than ours, I prefer to study emotional behavior in rats rather than emotional feelings. I study rats because you can make progress at the neural level, provided that the thing you measure is the same in rats and people. I wouldn't study language and consciousness in rats, so I don't study feelings either, because I don't know that they exist. I may be accused of being short-sighted for this, but I'd rather make progress on something I can study in rats than beat my head against the consciousness wall in these creatures.
There's lots to learn about emotion through rats that can help people with emotional disorders. And there's lots we can learn about feelings from studying humans, especially now that we have powerful function imaging techniques. I'm not a radical behaviorist. I'm just a practical emotionalist.