Yes you sure can, and they must be used carefully.
We've read from other recognition vendors that rely on monetary exchanges for employee recognition that say it will hurt "employee happiness" to have negative points. Quite the contrary, if the negative points is done in a funny, limited way, it can increase rapport. Teasing each other can actually make us closer.
When to use negative points
Men tend to tease their male friends, while women tend to use self-directed teasing (http://ihd.berkeley.edu/Ervin-Tripp%20Risky%20Laughter.pdf). This is something to consider when embedding a teasing badge into your program.
We have spoken with groups of male-dominated teams who find a "Thumbs Down" badge that is worth -1 point and can only be sent once a month can actually build rapport amongst the team. Plus, it is one way to get people to show up to meetings on time ;)
Philosophy & Psychology
The Recognize team does not believe in over-restricting companies. We are all adults here and if you want to have a negative point badge, then you can.
The recognition vendors who say they don't allow it for employee happiness are actually hiding their limited abilities with their monetary model. They can't manage the logistics of negative points, because that would mean the recipient would have money taken from them.
If you want employee happiness, then you don't want micro bonuses nor monetary rewards as the core of your recognition strategy. According to the research in social psychology and persuasion, micro bonuses will fail in the long term.
Dan Pink's TED talk in motivation proves micro bonuses is a loosing strategy - http://www.ted.com/talks/dan_pink_on_motivation?language=en.