People who cannot hear are deaf and people who cannot see are blind. What do you call people who:
[ul]
[li]Cannot smell things?[/li][li]Cannot feel the sense of touch? (Meaning they’re able to control their motor functions but can’t feel anything they touch)[/li][li]Cannot taste things?[/li][/ul]
Cannot sense touch = numb
Not sure about the others, or even this one; there probably just isn’t nearly so much of a need for easy terms of reference as there is in the case of blind and deaf.
Inability to smell=anosmia
Describing someone who lacks taste buds is tricky; “tasteless” is technically correct, but its connotations concern aesthetic incompetence or immaturity, not true sensory loss. The condition certainly exists: either the taste bud nerve clusters haven’t matured, or have been somehow damaged by virual infections. Also, severe enough anosmia affects the sense of taste as both are chemically-dependent and pretty robust. In fact, a loss of taste buds is often due to some difficulties with the sense of smell and the two are often hard to differentiate.
There’s probably an obscure name for it, I just haven’t run across it yet.
vertigo = loss of equilibrium, sense of balance
Cannot/will not speak = mute
Cannot speak can also be referred to as dumb. (Warning, don’t challenge them in pinball if they are deaf and blind also. They get mean.)
Numb usually refers to a specific body part. Paresthesias, on the other hand if you can feel it, refers to a general loss of sensation of pressure or pain.
I post this on behalf of my brother the M.D. who steadfastly refuses to sign up as a member. 
Loss of memory = amnesia
Loss of hair = alopecia
Loss of mental faculties = dementia
Loss of muscle due to lack of use = atrophy
My physics teacher made up the word “smelf” to mean “unable to smell” and he’s trying to get it to be used often enough that it makes it into the dictionary. So next time this comes up in conversation, feel free to assist him in this goal.
loss of muscle function = paralysis
loss of pain perception = analgesia
loss of ability to comprehend language = aphasia
loss of ability to recognize objects, persons, sounds, shapes or smells = agnosia
(may be extremely specific, e.g., prosopagnosia is the inability to recognize faces)
tone deafness = amusia
Being unable to speak due to a brain disorder is aphasia, being unable to speak properly due to a muscular/nervous/skeletal problem with the head or neck is dysarthria.
Being unable to understand the words of others is receptive aphasia, being unable to say the words you want to say (although you can think the words, you can’t say them) is expressive aphasia. Being silent because you just don’t want to speak is elective aphasia or elective mutism.
Altered sensation (e.g. tingling, pins and needles) is paraesthesia, being completely numb is anaesthesia.
Taste and smell usually go together- altered smell causes altered taste, but it’s definitely anosmia, not smelf! Solitary aguesia is much rarer.
There is also the syndrome present in some stroke patients where although they know that they have a left side and a right side to their body, the damage to their brain causes them to neglect one side e.g. they won’t see something on that side, if they want to pck something up that lies on their neglected side they’ll use their other hand, etc. This is known as hemisphere neglect.
Elective mutism–Someone who has the ability to speak, but chooses not to. It’s often seen in severely abused children.
Am I the only one who thinks this whole thread is senseless? 
I should’ve known to check the archives first. Nonetheless, the other answers here were… interesting
Thanks, all.