Yes, definitely. The bride should certainly get the groom a gift. Don't over-think it too much otherwise it will seem like an impossible task. Just think about what he would like. Think of it as similar to a special Christmas or birthday gift. I wouldn't worry too much about making it be something he can keep forever, an experience type of a gift is just fine, so long as it is a memorable experience.
Here are some ideas: a watch, or some golf lessons, or a monogrammed robe, or a collectible to add to his collection if he has one. A DVD that you think he would like would be a great option too (if you want to go this route, check out hubs from fellow hubber Cogerson - he has ranked sports movies, football movies, etc according to objective factors).