I'd take a look at the vacation policy and see what it says. Refresh my memory, so to speak.
If the policy is a "first come first serve" one, then you are well within your rights to request your vacations as you wish. Everyone has the same opportunity to be "first". I am assuming that you do not request them during the busiest times of your work year (ie-if you worked for a tax accountant, requesting vacation from March 15-April 15 would probably be a bad idea

).
If you want to be super nice, then, as a PP suggested, you could ask your direct co-workers (whose workload might be affacted by your absence) if they have any vacation plans for that time period, then you could approach your boss with "I'd like to take a vacation from July 12-19 and I have spoken to Mary, John, Joe and Bill and none of them want vacation during that time". The fact that your boss seems to be a workaholic who doesn't take vacation is moot. That's his/her decision to make, just as enjoying your vacation benefit is your decision to make.
When I first started working I ran into that situation. My uncle was retiring as a high ranking military official. The ceremony was scheduled for June. I told my supervisor the previous October that I would be needing that week off in June of the upcoming year. She gave me the same line of baloney "Well I don't know. What if someone else wants that week off? You might not be able to have it".
I pointed out to her that I was asking her WELL in advance (it was 8 months) and other people had the opportunity to do the same if they so desired. (We had a first come first serve request system too). She repeated that I would have to wait and if no one else wanted it then I could have it.
It aggravated me so I said to her "Let me put this another way. I won't be here for that week in June. If you want me to come back the week after, let me know. If you want me to leave today, let me know. But I see no reason why I should be the 2nd class citizen who has to wait for everyone else to decide what THEY want before I can request a vacation".
I wasn't the new kid on the block, I had already "paid my dues", I wasnt taking a vacation every other week. I was asking for one week's vacation 8 months from that time and she couldn't tell me yes or no in case someone else wanted it. I don't think so.
Thankfully she came to her senses and it all worked out. But I never really did understand why she thought that I should be the 2nd class citizen and hold off on my vacation plans until all other 60 nurses on my floor decided what they wanted.