Military discounts are part of your pay and benefits, so if they are offered then you should use them. I've noticed that most of the people who are timid about it in this thread are BDCP people. Once you work a few 100 hour work weeks in port or spend holidays out to sea with no extra money to show for it, you won't feel so bad about getting those discounts. So get them now because the Navy is going to get their money's worth with you and then some.
I do echo the advice to use your head though...in military heavy towns or upscale establishments, it's much less likely that you will get the discount. However, for movies/hotels/strip clubs out of your homeport area, use the military ID. EG: whenever I go to NYC to chill with friends from back home, I use the military ID and usually get the $20-40 cover waived. When I'm out in Newport, though, then a military ID gets you nothing. Just don't around expecting it or acting like you're entitled to it.
Regarding retailers, a lot of times the employees at retail places are trained to not give the discount unless asked, though, so you shouldn't feel bad for asking. Some google-fu will reveal a lot of big retail companies that give the 10% discount.
One time I went to the Met in NYC in my blues and not only did they give free admission to me and everyone with me, they gave us discount coupons for the restaurant.
The Met, along with most if not all NYC museums, is technically free for everyone; they just have "suggested donations." You would get funny looks from the employees for it, but you could pay $.25 if you wanted and have every right to walk into the museum.