I've always gone with the one-week rule for opened packages of meats, but I don't know if it applies to pepperoni too. My kids loooove turkey pepperoni, and there have been a few times that they've inhaled the rest of a package before I remembered that we probably shouldn't have eaten it!
We haven't gotten sick yet, knock on wood. Maybe the amount of salt and preservatives in the pepperoni (as compared to sliced ham, for example) keep it safer, longer? If it were me, personally, I'd freeze it and use it later. That may not be the technically correct answer, though.