Why use a router at home
If you use a router at home, you're going a long way to ensuring that your computer is protected from malicious software. If you don't have a router, you should really consider getting one. The reason is because when you connect your computer to the internet, you're potentially exposing yourself to service attacks. When you surf the web, your web browser creates a connection to a web server to download a web page. Imagine that you point your web browser at http://www.google.com. Your browser will contact a program at Google called a web server. Your browser sends it a command to retrieve a page, and the web server responds with the page itself. The browser needs to know how to contact the web server. The URL you entered (http://www.google.com) provides the browser with the information it need to contact this web server. It includes, for example, the name of the machine to contact (www.google.com). The machine running the web server may also be running services other than the web server. It might, for example, be running a service that accepts emails. Internet clients distinguish one service from another by an identifier called the port. There are many "well known" port numbers and services can even choose to ignore the web known port number and use an entirely different port number. The well known port number for web servers is port 80. You can generally specify the port number in a URL by appending it after the name of the machine as in http://www.google.com:80.
Services, like web servers, that need to accept client connections, can listen on a port. If you connect your PC directly to the internet, and you have one of these services running, other people on the internet may be able to connect to one of these services. PCs and the operating system that run on them were designed to be flexible, so you can easily install software that runs one of these services. If your PC is connected to a router however then the router acts as a go between for information going to and from the internet. Internet traffic doesn't go to your machine unless the router explicitly sends it there. In fact, if you want to run a web server from your PC you have to go into the router configuration and tell it that it's OK to forward the traffic.
To get an idea of which services are running on your PC, open a command prompt and type "netstat -a". Lines ending in LISTEN indicate a service that is listening on a port.
You can find inexpensive routers for around $40. I had a Netgear router that went down like a cheap whore. I replaced it with a Linksys one and haven't had to reboot it since I installed in. The WRT54G sells for $50 at Amazon but I expect you should be able to find it for less at your local discount computer store.