Pros
The pay is pretty good and the benefits are very good. Not many civilian companies give 30 days of paid vacation per year, unlimited sick time, flexibility, chance for advancement, and free/cheap healthcare. Although not always perfect, there is a definite career path and chance for advancement. Promotions aren't guaranteed, but if a person works hard, does well at their job, and continues their education, there is an excellent chance for advancement. One nice thing is that a person usually has flexibility throughout the day or week to take care of things if needed. As long as your job gets done you don't usually have somebody watching you to make sure you've worked a certain number of hours per week. This of course depends on the job. If you are a security policeman and assigned a certain shift then you may not have as much flexibility to go and take care of something because you have to man your post.
Cons
The disadvantage is that you can't just decide to quit anytime you want to. Sometimes long hours are involved, including deployments away from family. There are politics within the military, but I've found that to be true in the civilian jobs I've had as well.