I honestly doubt that the admissions really care about what minors we have. This is probably supported by the fact that there isn't even a space for it on the application. However, a minor can be positive, but not in the way that you think.
When I was choosing a minor, I was looking for one that would stand out at some place in my application. I was deciding among minors in: Applied Developmental Psychology, Accounting, Biomedical Research, or Public Health.
A minor in Applied Developmental Psychology had an internship component to it, in which I would work at a daycare/kindergarten. I think this internship could accent my app nicely.
With a minor in Accounting, I would be able to take a lot of Business and Management classes. While the admissions wouldn't see my minor, they would see the classes, and thus my academic variety.
The Biomedical Research minor (which I am currently applying for), as its name implies, involves doing research for class credit. This has its obvious benefits.
Finally, the Public Health minor... While it may sound worthwhile, this minor does not involve any "special" components to it. Thus, I didn't consider it for too long.
As you can see, minors can add another dimension to your app. Should you be so lucky that your school offers minors with such notably unique characteristics, it would be advisable to take one up. Otherwise, minors don't carry much weight, except for the extra course load.