Is there a vaccine for adenovirus?

Not exactly. Adenovirus is a family of 40 different virus' that each cause severe cold-like symptoms. At one time the military did in fact have a vaccine and routinely immunized solders because the virus caused them alot of downtime. However, it was a live vaccine and caused do many side effects that they lost more time on active duty then if they had caught the virus itself. Today, the best prevention is good hygiene.