It's hard to say from what you have written if the problem in the corporate culture, a few judgemental employees or bad habits on your part.
If no one else is using leave at all, it is likely a corporate culture thing and the best thing you can do is get out. A company that thinks it is a bad idea to take vacation is a company that thinks you are as interchangeable as the desks and doesn't recogize how unproductive tired people are. They are offering an unusually high amount of vacation (many people in the US only 1-2 weeks vacation for at least three-five years with the company), so they realize it helps recruit, but if they don't let you use it and they don't pay you for unused leave, then they are are just playing with you. I suspect this is not true at your company becuase your boss apparently didn't have a problem approving the leave.
If there are few people who complain but you have seen others taking leave, then the problem is either how you go about using your leave or the other people's attitude.
You can't fix their attitudes, but you can look at making sure that your vacation is not causing them to have problems and you can make sure your boss is prepared for any complaints that come his way.
You should also talk to your boss about the complaints you are getting to make sure he isn't getting a bad impression of you from these people. Since you have an unusually high amount of leave, it is possible that you negotiated this or they decided to do this for new employees only to get better recruits. In that case, the others may not have as much leave as you do and that could be what is causing the resentment. Talk to your boss about it and see if he can give you any insight as to why these people have a problem with you using the vacation. And by talking to him, you may be protecting yourself from their pettiness because he will realize what is at the root of any complaints they may have about you.
But as to what you personally can do to lessen the chance of others having a problem with you taking your vacation:
First plan your vacation days in advance (saving a few for personal emergencies if need be). I generally plan my vacation time at the beginning of the year and for any chunks of more than two days that I plan to take, I put in the request as soon as I know the dates I want. This allows people who are planning resource availability the notice they need to make sure that deadlines are not affected by this. If they know in February that you are taking a week in September, they can plan around it. If they find out a week ahead of time, they can't. Next, make sure you tell people not in your direct approval chain about the leave well ahead of time. Put it on a calendar that they can see.
Make sure to prepare for the leave by getting with the people you work with and making sure everything you need to get done before you go is done (and checked into source control if you are a developer). If you have something that you know can't wait until you get back, make sure to get with the project managers and have someone else assigned to work on it while you are gone. I never take a whole week off without a meeting 1-2 work days before the vacation to go over with my boss or project manager (or usually both) in detail where each project I am working on stands and who will be the contact point if something comes up while I am gone. Information sharing is the key to being able to take a real vacation without others complaining.
If you need to take a vacation without a lot of advance notice, make sure it isn't right around a major deadline unless it is a genuine emergency (and make sure that the complainers know it was an emergency). I'll never forget how angry we were at one employee who was supposed to be writing requirements and she wasn't finished when she went on a one-week last-minute vacation a week before a deadline. Really hard to write code when the requirements are last minute anyway, impossible to write it and meet the deadline when no one can even tell you what the requirement is. Of course the devs got blamed for missing the deadline which made us all the angrier at her. So don't put your colleagues in this position.