We take it for granted that intelligence can be built orthogonally to emotions, but neuropathologist Antonio Damasio would beg to differ. In several books he has argued how emotions are integral to human consciousness, and that consciousness itself may not be possible without emotions. Obviously, nobody has an ironclad proof of this thesis, but I find it at least plausible.
Living creatures defy the second law of thermodynamics by actively expending energy to avoid their dissolution. This process is called "homeostasis", and is why you eat when you are hungry, sleep when you are tired, and pee when your bladder is full. It's also why you shiver when you are cold, sweat when you are warm, and release insulin into your blood stream when you eat. The idea is that the external environment and internal processes are all causing chemical concentrations within the body to go out of balance, and so other processes kick in to restore the balance. To do this, the body must have a way of knowing its internal state. And because the internal state of every body is peculiar to the unique characteristics of that body, this sense of internal state is the most subjective experience one can have. It may be the entirety of subjective experience (modulo obvious factors like occupying a position in 3-space that cannot be occupied by other bodies).
Damasio's claim is roughly that emotions are high-level sensations of homeostatic processes occurring within the body, and thus, are an integral and necessary component of any agent that maintains homeostasis. The robots we build today don't have nearly the level of homeostasis that living creatures do, because they are very brittle and solid. They generally don't regulate their internal temperature and have no analogue to blood pressure, blood sugar, or the like. Surely they monitor energy levels and proprioception (positioning of limbs, orientation in space, etc.), but they most homeostatic thing they do is perhaps balancing on two legs.
If future robots incorporate more wetware, it is likely that they will require more biomimetic homeostatic processes, and these will begin to look more like emotions, which we share with lower creatures that have no language or tool building.
We need to sense emotions in order to fix an internal imbalance. But we need to show emotions because communicating internal state can be an essential component of social interaction. Demonstrating fear visibly can cause an aggressor to deem one not a threat, and cease an attack. A threatened attack may be sufficient to obtain submission, and is much less risky than an actual attack. Demonstrating hunger is obviously important for infants and young, as is demonstrating illness. It should be obvious that bonding also requires the communication of internal states, as well as many higher-level interactions like cooperation or alliance.
Finally, if androids are to be humanity's servants, they must be able to understand humanity's needs. A good butler/waiter/conceirge is not a dumb order-taker, but rather someone who can perceive a need and suggest a solution even before the client is aware of it. This is not possible if the servant cannot read and comprehend the emotional state of the client. In order for an android to truly serve a human at the level of emotional needs, it must understand those emotions on an intuitive level. Basically, it must feel them, somehow. To truly understand an emotional creature requires empathy, and it appears that this capability exists among many, if not most mammals, and even many birds.
So, I reject the notion, common throughout sci-fi from the very start, that anything approaching human-level intelligence is even possible without a first-class emotion subsystem. Even if an alien intelligence could be built without emotion, I don't believe it is possible for such an intelligence to truly understand humans or other higher creatures on earth without emotional capability. I certainly don't think it is possible for an android that regularly interacts with humans via language.