Yes, except possibly the deaf and hard-of-hearing (this depends on level of hearing impairment). The "tone-deaf" or "monotones" can be taught to sing by matching pitches, as someone mentioned above -- often tone-deafness is merely inattentive listening to pitch, sometimes caused by fear or anxiety. Normal human speech uses a range of pitches, so we all have the capacity to sing, unless we cannot hear.

There is a good description of how to teach "tone-deaf" people to sing in W.A. Mathieu's book, The Listening Book (Shambala). It's the chapter called "Tone-Deaf Choir."

Also, the singing voice responds to stress, illness, emotions and thoughts quite strongly: I have found that the more I am present with my thoughts, emotions, physical states etc. the better I sing -- if I know I am tired or ill I can sing in those states if I need or want to as long as I acknowledge that I'm tired or ill and take steps to enhance my singing: for instance, I once went to a ballad camp with a heavy head cold and was able to sing for two nights until three in the morning by drinking quart after quart of water. Take care of your voice and it will reward you. Pay attention.