What are the (possible) cons of allowing a stranger the use of one's wireless internet connection?

A few hours ago my neighbors asked me if they could use our WiFi for a few days.
I told him I wanted to think this over, and discuss it with my girlfriend, before I would say yes or no.
We don’t have a particular relationship with our neighbors (other than that they annoy us every now and then with too much noise, and my helping his girlfriend with some small practical things), and I don’t have reasons to believe they would use it for any thing else than the purpose he told me (he wants the connection for a about a week, to watch foreign tv stations).
But I think I’ve been spooked out in the past by alarming articles and news items about internet safety, identity theft, child porn, downloading illegal stuff, etc.
My question is the following:
Is it safe (or not safe at all) to allow ‘a stranger’ usage of one’s wireless connection?
What are (possible) cons?
Edited to add that my girlfriend is a fierce online game player (Warcraft); will an extra user on my connection decrease the fluency of her playing?
Thanks in advance!

Edit: Would you allow access to your WiFi to ‘a stranger’?