Are you going to be applying to just medical schools or to combined programs like the MD/PhD or MD/JD routes? You definitely don't need two undergrad degrees to be an excellent candidate for med schools, provided that the rest of your application is strong, but if acquiring another related degree (such as completing a double major) is relatively easy for you to do, then it certainly wouldn't count against you and could be useful in the future, depending on your career choice. Of course, you wouldn't want to jeopardize getting a great GPA or valuable MCAT study time just for the sake of having two degrees, so it's definitely important to consider the amount of time you would realistically have to devote to getting this second degree, as well as how many additional credits that would be needed.
For the combined programs, having another degree that you can actively apply may give you a very slight advantage or be an interesting point to discuss during interviews (at least, this is what I have been told by advisors at three separate institutions. I am not an expert on this, so it would be wise to consult those that actually are).
If this second degree is something that you are exceedingly interested in and you know that you will do very well in, it could certainly be worth pursuing and achieving. Just make sure that the positives outweigh the negatives 🙂