Are there emotions that only some people can feel? Presumably, there are emotions that almost any person can feel, such as happiness, sadness, guilt, and embarrassment.


But are there emotions that only a small fraction of the population can feel? 
How might it be established that an uncommon emotion existed?
There is strong evidence that there is indeed a interindividual differential distribution of emotional processes or capabilities.
For instance, Bartels and Pizzarro (2011) could show that some antipersonality traits connected to the lack of compassion and empathy towards others are varying among people. Those who endorsed a more pragmatic and "straight" (utilitarian) view of life scored lower in social (and hence empathic) questionnaire batteries.
When people are asked about their spiritual attitudes and habits and what emotions they connect to this, they respond very different. For example, mystical experiences - the strong feeling of oneness with the environment - are more likely to score on altruism and empathy (no reference ad hoc present). A more "realisitic", grounded person would deny having such feelings simply because his or her internal self-construction processes do not attach with the same strength to those emotions. They would have different emotional attachments. 
A very simple, common and intuitive (needs not really a scientific approach) illustration is when you consider "self-confidence" as an internal state. This is obviously a dramatically varying emotional state in humans. Overconfidence evokes internal security about own capabilities and the feeling of "i can master that", in contrast to a lack of confidence. 

So, people have different default emotional states and they evoke different feelings in themselves due to different interaction with the environment. 

References


Bartels, D. M., &amp; Pizarro, D. A. (2011) The mismeasure of morals: Antisocial personality traits predict utilitarian responses to moral dilemmas. Cogntion PDF