Which Linksys model do you have? They can be considered a firewall because they block open ports. If you haven't modified your port forwarding settings, you have no open ports on the internet (which is a good thing). You'll be protected from viruses such as Sasser that scan the internet for open computers.
Other than that, though, it won't do too much. If you're worried about programs on your computer accessing the internet, try a firewall such as Norton or McAfee (or even Windows XP's built in firewall). They will let you know when something wants access to the internet, what it's doing, etc, but they often take more time setting up.
Hope that helps!
