Common col. Too many different viruses can present with symptoms of the common cold.
Two reasons why... First is that there are several thousand viruses and each would requires a specific vaccine. This also does not take into account viral mutations that often occurs. Second is that the common cold is not fatal and thus there is not a need to spend limited healthcare dollars on a non-fatal, nearly harmless condition.
Too many viruses. The problem is that the common cold is not merely one disease. What we call the common cold is actually one of thousands of viruses. With each cold we become immune to that particular virus but there are many left to take its place. We simply cannot make enough different vaccine to covre the shear number of different viruses involved in the cold.