Capitalized:
* As part of a proper noun: "United States Marine Corps," "Marine Corps Recruit Depot Parris Island," "Marine One" (the presidential helicopter).
* Referring to a specific individual: "My father was a Marine."
* Used as a title: "Sergeant Marine, sir."
Not capitalized:
* As a general term: "He served in the marine infantry."
* Used as a synonym for "sailor": "The marine life in the coral reef is amazing."
In summary:
If "Marine" refers to the U.S. Marine Corps or a specific individual serving in that branch of the military, it is capitalized. Otherwise, it is not capitalized.