Just as in humans, most vaccinations cause at most very mild outward symptoms after the vaccine is given.  Some horses may be a little more lethargic than usual, have some mild tenderness at the injection site, or stiffness in the neck if that is where the vaccine was administered.  Occasionally, the horse will develop a mild and transient fever, and this is usually noticed if the horse goes off his feed.  These usually resolved uneventfully, although sometimes anti-inflammatories are given.