My knee-jerk reaction is that the most likely suspect is keratosis pilaris:
http://en.wikipedia.org/wiki/Keratosis_pilaris
However, this is based solely on the facts that keratosis pilaris affects such a high percentage of people, and that so few people know what it is so it's often mistaken for other things. I, myself, have had these bumps on my arms and legs since childhood and even dermatologists never told me that this was the name for it. At any rate, obviously there's no way I can even hazard an accurate guess at something like this over the internet because I can't see it, but there's my 2 cents. (Your mileage may vary, may only be worth a penny. LOL)
My son is covered in bumps on his arms, back, neck and face but we believe that it's a reaction to Midodrine. His doctor isn't concerned.