As mentioned above it varies company to company. Where I work you arent allowed per se but I am carrying 5 days into 2010 as I am going skiing at the end of January so I will be using them up quickly.
Similarly if you are getting married or anything like that in the new year companies usually make an exemption.
However, I would recommend going to your direct team lead and or department manager first, rather than HR, and get it OKed by him/her first. HR don't really have any clout at the end of the day and are just gonna give you the speil from the employee handbook to fob you off if you go directly to them first (based on my previous experience of HR staff).