I already have Avast (free) running on my comp. However, I want to get a keylogger on here because I think my roommate is using my computer when I'm not home and I want to check.

I was thinking of getting this
http://www.remote-pc-spy.com

But how does this keylogger run with Avast in the background? Like can it be an exception
Is this keylogger safe to use?

In regards to your first question, yes, you can run keyloggers with Avast installed you'd just have to go into the main interface and tell it which files and processes to exclude from malware scans.  I'd probably just stick to the basics like the ones available on BT4 rather than shelling out cash for a commercial, and possibly malicious, tool.  Its your own system you're installing this on so you wouldn't be overly concerned with hiding it from the anti-virus via rootkits and such.

In regards to Mark's point, while the above guidance is technically possible, it may not be the smart move, the appropriate move, or the easy move.  What exactly is your main issue?  If you don't want your roomy on your computer then password protect it.  If you're more worried about him getting at the data on your system then start looking at encryption. (a container or whole disk) Whole disk encryption would also help keep him off the computer in general if you think he's got the skill to bypass a standard login. (via something like a live CD or bootable USB) 

Do you have some reason to go the keylogger route?  If your goal is to just keep him off the system there are better ways then going into spy-vs-spy mode.

One quick thought - how about a possibility where your friend already installed a key-logger and spying you? Think about it

Its a commercial tool , why dont you contact the company's support for the question . I think they will be the best to answer it with guaranty .