In my opinion the words are used in the following contexts:
1. Rather than - Indicates some sort of preference over the other. "I think we should eat rather than dance"
2. Instead of - Indicates some sort of replacement function. "I'll have french fries instead of pizza"
3. In spite of - Indicates some sort of contrast between two things. "We went out in spite of the thunderstorm", and I think despite can be used interchangeably with in spite of.