It seems we like to tell one another that it is important to feel negative emotions, like sadness or confusion or grief, because it is an important part of being human. Is this really the case, or could we just as well do without grief and despair? Conversely, is it also an important part of being human to feel rage, or hatred towards someone or something?

There are two ways to read your questions: 1. Would we be better off never feeling negative emotions because they were never called for--i.e., because we never experienced the sorts of events that make grief or anger an appropriate reaction? Or... 2. Would we be better off never feeling negative emotions regardless of what happens to us? I am inclined to answer 'no' to the second question. While some (e.g., Stoics and Buddhists, at least on an oversimplified reading) suggest that we should approach negative events with a level of detachment that make grief, anger, or despair inappropriate, and the wise or enlightened person will reach a point where she can avoid feeling such emotions, I find that approach inappropriate. I think it would be both mistaken and almost inhuman not to feel grief at the death of one's child or not to feel some level of anger at the terrorists who perpetrated 9/11 (whether despair is ever appropriate is trickier). So, I do not think we would be...

Could a robot, imbued with artificial intelligence, feel emotion? And could it feel the desire to improve its lot in life - e.g. if it was a servant robot, could it feel the desire to overthrow its master, escape the humiliation of being a servant, and possess things for itself?

I don't see any reason that a robot could not, in principle, be built that would be conscious and feel emotions. Some people (John Searle, most famously) disagree, at least about an artificial system that does not replicate our brains' "causal properties". However, I don't think we have any good ideas about how to create consciousness in robots, in part because we don't have any good theories about how consciousness in humans works. It's always possible that human consciousness only exists because we have something robots could never have (e.g., immaterial souls, although it's not clear why it is impossible robots could be endowed with souls, or our particular biological materials). But it seems more likely to me that our conscious experiences and emotions (including our feelings to improve our lot in life, our desire for possessions, our desires for freedom) are the product of complex processes in the brain that could, in theory, be replicated in a non-biological system. It seems likely to...