Pros
A proud and patriotic organization, generally takes care of its people and strives to reward performance. Surprising amount of autonomy if the job (and boss) requires; career is in your hands. Lots of good options (many not advertised...again its on you) outside of the typical career tracks. A close fraternity, work hard and play hard. Paid fairly well, won't get rich but comfortable.
Cons
Gone from home sometimes for long stretches (many months), often doing less-than-glamorous work. The navy accepts all types so you are often dealing with the personal and financial problems of folks who at other organizations you could easily fire. Can be frustratingly slow and lots of gov't inefficiency. Locations, spouses working, etc, the needs of the navy ultimately come first.