In humans, there are 6 basic responses i.e. emotions which are rooted in our physiology. These cause an instinctive response in our brains and bodies, not just in our minds. These emotions are linked to particular brain areas in humans or to hormonal or chemical responses. They are survival responses to protect us from adverse conditions and to make us seek out favorable conditions. Most are linked to our perception of comfort and discomfort. It is likely that cats have equivalent physiological responses to the same, or similar, stimuli.
A self-preservation instinct. Fear leads to alertness, caution and possibly to flight. It prepares the body for flight or defense. Fear is the recognition of a potential danger rather than the instinctive (and possible energy wasting) flight from potential (rather than actual) danger. Fear allows the animal to assess how real or immediate the danger is and to take appropriate action (flight, freeze, hide, disregard etc).
In the human context, originally this prevented us from eating contaminated food or coming into contact with filth. In modern humans it is also applied to other stimuli (the thought of doing something, an image or a situation). It is an avoidance mechanism. In cats, whose livers are not good at dealing with toxins, the avoidance of stale food is probably caused by a similar mechanism. Cats rely on smell, taste and "disgust" to avoid tainted food.
Associated with the basic mating urge without which we would not breed. Desire is associated with pheromones and body language; and causes chemical reactions in our own bodies when we experience it. It is associated with mate-seeking, assessment of a potential mate's suitability and courtship behavior rather than just with copulation.
A form of psychological discomfort experienced in non-ideal situations; it helps us to avoid non-ideal conditions. Humans have a wide range of sadness-emotions varying from grief, transient upsets and some forms of depression (a chemical disturbance in the brain) have symptoms like sadness. Cats exhibit depression in some situations and some cats have been reported as "inconsolable" when a close companion dies. Separation anxiety in cats and dogs may be partly due to the sadness mechanism.
A form of psychological comfort/satisfaction experience. It helps us seek ideal conditions or repeat beneficial behaviors (eating, sex); chemical reactions are involved - feel-good chemicals are released in the brain. In cats it is most often seen as "contentment" and is also evident in cats and kittens during play. Play is a self-fulfilling behavior which produces "happiness" by release of feel-good chemicals.
A reaction to a non-ideal situation when we intend to fight; chemical reactions occur in the body as part of the fight or flight response. It can also result in displacement activities such as self-mutilation. Cats which are handled against their will exhibit obvious anger. Most vets are familiar with sheer feline fury though it is hard to distinguish "anger" from the "fight" reaction. "fight" is relatively transient; anger (a bad mood) does not pass so quickly (a cross cat will stay angry even when the stimulus is removed).