In physics, having a degree in math as well helps for obvious reasons. But anyone who's familiar with theoretical physics knows that this is especially true for that particular branch of physics. Anyone who truly wants to go into theoretical physic would be foolish to not double major in math. Since theoretical physics was my original goal, I chose to double major.
Also, when I was in high school, I had been working with a professor who was testing me on a bunch of different subjects and giving me books to read. By the time I reached college, I was already on the level most math majors are when they are in their third or fourth year. So adding a math major didn't add very many extra credits to my requirements.
As a matter of fact, at my school, if you choose to get one degree with two majors on it, it doesn't change your number of credits required or the amount of time it takes to graduate at all whatsoever (I don't know if this is for any two majors or just for two majors under the same college). So it kinda doesn't make sense to NOT double major since it takes the same amount of time, effort, and money as a single major or a single major plus a minor. Especially if your second major is relevant to what you want to do in your career (like a theoretical physicist getting a math degree, or an applied physicist getting an engineering/computer science/applied math degree. A lot of people here pair political science/criminal justice/history [two of those, or sometimes even all three] together).
When I first got to college, I decided to get two seperate diplomas instead of one degree with two degrees listed. That's 32 extra credits, but considering how far I was in math, I was still going to graduate within four years (until personal issues caused me to screw up two years worth of schooling). I'm in a position now where getting two majors (but on the same diploma) and getting a masters degree on top of that wont take me any extra time compared to just one bachelors degree in one subject. Additionally, having a masters in math should make my application look better when I'm applying for grad school in physics. After screwing up an entire years worth of grades, then not going to school for a year, I want every advantage possible, big or small. Also, I love math so much that I'm overjoyed at the opportunity to take these grad level classes that I otherwise wouldn't have had much access to.
And then there's the fact that I'm not even 100% sure which direction I want to go. I'm leaning more towards physics than math, but I've never been absolutely sure about this. I may decided to go the math route, in which cases already having a bachelors and a masters in the subject is going to be beneficial. So now I have more flexibility to change my mind. I've seen grad students who wanted their masters in something they didn't get their bachelors in, and they usually seem to struggle.
And like a few others have mentioned, it does make your resume look better. In some cases, maybe only a little better, but better is better.