Even when dealing with publicly available information...here be dragons.
First and foremost, can you prove beyond a shadow of a doubt that the online presence is actually the person in question? Between people that look similar and/or share names, and some simply downright nasty trolls, it's possible that the person that posted such things is not the same person that is applying for a given position. Make sure you're making the right connection.
That said, it in part depends on what actually constitutes a "negative online presence." Defaming a current or past employer is one thing, and pretty obviously should be considered. As Chad said, such behavior can be a cancer in the workplace, poisoning the whole group. Getting drunk with friends is a different matter (so long as it is legal and doesn't interfere with work), and in my opinion, it's ludicrous to think that just because you can't see evidence of it, that no one else in the company does the same thing once in a while.
Additionally, make sure that you're not attributing behavior of your prospective employee's friend/family/acquaintances to your employee. It's easy to say "well, if my other employees do it, they're smart enough to not plaster it all over the Internet," but what if your prospective employee didn't put up those pictures (because they, too, are "smart enough to not plaster it all over the Internet")? What if someone else at the party took and posted the pictures, and someone else tagged the employee? The employee didn't post those pictures, and they have no control over the person who did. Should the employee be faulted for someone else's actions?
tl;dr - It's a sticky matter. Make sure you have your facts straight, and don't hold them to an abnormally high standard solely because you happen to have knowledge of things they do that you don't necessarily approve of as a person. Remember that they're human, that your other employees probably do many of the same things, and a given person can't control what others put online.