Facebook can get pretty cranky on this.
Basically if you want to interact with Facebook you must set up a personal account.
Once that is done you can set up any number of Facebook pages for business using you personal account. You can also, as pointed out by bill, add existing facebook users as administrators on any pages that you create.
What you can't do.... Or at least what Facebook don't want you to do is.... Create a personal account under the guise of your business, create a separate personal account just to manage your business account, or finally run a personal account as your business.
If Facebook come across anyone running these things the account will be suspended.