The Karate Kid (1984). This is a classic that was actually written by a Sandan (3rd degree black belt) of Shorin Ryu. This movie not only goes along with the virtues and ethics taught in Shorin Ryu, it also includes great metaphors about training, learning, and life.
The 36th Chamber of Shaolin. This movie is great because about 80% of the film is the main character training, Unlike other movies where the character is either already a tough guy, or becomes a masterful martial artist through artificial means, this character San Ta trains diligently for years to become a true martial artist.
The Forbidden Kingdom. There is a lot to say about this one. First of all it's the first and only movie so far to include both Jackie Chan and Jet Li. Also, it delves into the philosophical side of training and is partially based on ancient Chinese folklore which is always fun.
Fearless. Fearless is based on a true story and parallels situations that many talented martial artists face. At first, the character thinks that being the best martial artist simply means being able to beat any challenger, but through training and getting through tough times he realizes that it's really about doing the right thing and helping others however he can.
Crouching Tiger Hidden Dragon. This movie contains a lot of fantasy and a lot of amazing reality at the same time. While there are characters that can essentially fly as they fight, the masterful main character is also well versed in Chinese herbal medicine and the ability to both harm and heal utilizing meridian theory as martial artists do. This is also a very philosophical movie.
*Note* I'm not endorsing these movies for people of any age. I do recommend that parents look up these movies on imdb.com which has a great feature that lists anything that can be offensive/inappropriate in a movie right down to the exact number of swear words.