Is self-consciousness an integral part of consciousness? Do animals posses a self-consciousness? To answer these kinds of questions we need to understand the phenomena of self-consciousness first.
What is commonly called self-consciousness (even in philosophy occasionally) is really two distinct phenomena. On one hand we have what I call the self-model. Basically the self-model is how we mentally represent our selves, it contains information about what motivates us, as well as information such as how we might look to an outside observer. The other phenomena that is sometimes called self-consciousness is self-awareness. Self-awareness is much less abstract than the self-model. In the simplest possible terms self-awareness is the process by which perceptions and knowledge are felt as being part of us. When you are hungry you feel the need to get some food for yourself; it is self-awareness that is responsible for the knowledge that this feeling of hunger is our feeling and that we need to do something in order to satisfy it.
Let me describe a bit more thoroughly the self-model. I have described mental models in some depth earlier (see here), and the self-model is one of them. The self-model then is the model that represents how we think, feel, and reason in general, as well as containing some information about how we appear to other people. For example our conceptions of our self, such as “I am a rational person”, or “I like coffee”, are part of our self-model. You might say that these are simply facts, and thus not necessarily part of the self-model. While it might be the case that some of the information that makes up our self-model are facts it is easy to see that this is not always the case. For example someone may think “I am a rational person” but then act in irrational ways. Rationality is part of their self-model, but it is not something that seems to motivate them, and thus the statement “I am a rational person”, although part of their self-model, is not a fact. Generally however I would assume that the descriptions of ourselves that our self-model contains are fairly accurate. The self-model for the most part seems to contain descriptions of our selves that we either consider ideal or have been formed from experience of our own actions, and thus it is likely that it reflects how we actually act in most cases. Besides these self-conceptions our self-model also contains expectations of how others view us. Some of these expectations are purely physical, for example my self-model contains information that says other people will see me as sitting down in a certain place. Other expectations may be more abstract, for example my self-model also contains the information that other people who read my work will see me as someone who is interested in the philosophy of mind. In general the self-model is complex, abstract, and created over a long period of time.
Now let us turn to self-awareness. As I mentioned above self-awareness is closely tied to our perception of the external world and of our own internal mental states. It is not simply perception though; it contains the knowledge that these perceptions are mine, and not someone else’s. Although I can’t provide you with an objective explanation for the cause of self-awareness it is quite easy to demonstrate that it exists. Consider a man who has been for a long time without water. Let us allow that he has the perception of his thirst but no self-awareness of this perception. If we presented this man with a glass of water then he has no special reason to drink it. Yes, he perceives thirst, but if he doesn’t realize that it is his thirst, so why should he be motivated to drink? Because situations such as this never actually arise we can be reasonably sure that we all possess self-awareness. Let me use an example to help distinguish this self-awareness from our self-model. My perception that I am sitting down is a good example of self-awareness. It is true that the more abstract information about this event, such as what it might look like to someone else is part of the self-model. However the direct perception of the feeling of sitting, and the knowledge that I am the one doing the sitting, is self-awareness. Thus, in contrast to the self-model, self-awareness is immediate and tied to perception.
Before we answer the bigger question about the relationship between consciousness and self-consciousness let’s look at the possibility of animals being self-conscious. It seems pretty clear to me that most animals lack a self-model or possess only a rudimentary one at best. For example a parakeet can be fooled by a mirror into thinking that it has a friend with it, so clearly it lacks a self-model that contains expectations of how the parakeet looks to an observer. Self-awareness however seems much more likely. If you think that animals are conscious in any way then it seems obvious that they must be self-aware, since they are motivated by their desires as much as we are. So are animals self-conscious? Yes and no.
So then is self-consciousness necessary for consciousness? If we accept the idea that animals may be conscious but not intelligent (see here) then it is obvious that the self-model is not required for consciousness. Self-awareness is much trickier however. It is my intuition that self-awareness is found wherever consciousness is. For example consider cases where self-awareness is lacking (alien limb syndrome, unilateral neglect, ect). In these cases, as far as I know, the person is no longer conscious of the perceptions that they have lost awareness of. The patient suffering from alien limb is not able to feel sensation from the limb that they are claiming is someone else’s. They lack self-awareness of their limb, and perhaps because of this they have lost all conscious perception of it. Perhaps then self-awareness and conscious perception go hand in hand, such that to consciously perceive is to know that the perception is yours. Under this view without self-awareness all perception would be unconscious, and thus there would be nothing to be conscious of. However I must admit the possibility of finding evidence to the contrary that would disprove this assumption, so at this point the role of self-consciousness in consciousness is not completely settled.