You can protect your broadband access. The only significant risk to leaving it open (assuming your computer has firewall, etc, which it should, to be protected from the net) is that people might do illegal things using your broadband, and then you might get into trouble. I think the risk is pretty low, though.
Oh, if you don't encrypt the data between your computer and the wireless, it is true that your neighbours could see everything you do online. It's unlikely they have the technical skills, though, or could be bothered.