Loki, it looks good. The basic structure is quite good, you just need to clean up some silly writing errors. I agree with GreenLantern that the statement makes no sense without an explanation of why you didn't go on to NROTC/USNA from NJROTC. I'd put a brief explanation where your second to last paragraph is, since that ¶ totally destroys the flow of the statement. It says some nice things, but not things worth inserting in a paragraph completely unrelated to the ones that precede and follow it.
Opportunity, freedom of speech, freedom of religion.
Use periods rather than commas.
A few of the many privileges that the United States has granted my family and I.
You've already broken the rules for effect in your opening. You might want to add "these are" to make this a sentence.
I wish to repay this country for all of the luxuries–luxuries that I’ve seen first hand what other countries could never offer–that it has provided for us.
-Contraction
-You mean "that"?
I do not remember much from my childhood, but the one thing that I remember most clearly was when my dad asked me what I wanted to do when I became an adult–I told him I wanted to be a pilot.
This I'm not sure of... it may not even be a rule, but I'd put a space on either side of a dash. It's just easier to read.
Joining the Navy and earning a commission was not part of that dream until I joined NJROTC in high school.
I want to say this should be "were," but I don't know and I can't find proof either way.
NJROTC taught me to be strong and confident by participating and leading my unit through many events such as: Competitions, Area Eight inspections, community service projects, and raising money for our unit trips.
You don't need the colon and "competitions" shouldn't be capitalized.
Without the courage and strength that my instructors taught me, I would not have been able to lead the Color Guard and perform outstandingly in front of hundreds of officers in the Navy and Marines.
"Outstandingly" would not be my adverb of choice. I didn't even think it was a word.
If it wasn't an officers-only event, you'd better say "Sailors and Marines." (And adjust the head count as necessary)
NJROTC was not only fun for me, but it taught me the core values of the Navy. Values which helped me stay drugfree, kept me very active during high school by participating in my community, and attaining my current job.
This is the only part of your statement that is truly bad (and I didn't even notice on the first run-through). You need a dash after "Navy" (and then this thing would probably be too big), for one. You said, "Values which... attaining my current job." I assume you meant "kept me active ... by participating in my community and attaining my current job."
But I don't think there's any tinkering you could do to make this structure work. Rewrite or delete.
I wish to join the Navy to continue to better myself as a person and also to provide my devotion, leadership, experiences, and skills that I have acquired.
I think you took it just a bit too far there. It's better without that last bit.
As a first generation college student, and hopefully an officer of the Navy, I wish to start a tradition that my children and their children will continue.
I'm not in love with this bit. I think you can write it better.