I will recommend that anyone on a high-speed Internet connection obtain and configure a router. The router is a physical, and virtually impenatratable wall between the Internet and your PC. While there are software solutions available to protect you, the very nature software means it can be compromised by user-error or inherent flaw.
A router plugs in between your DSL/Cable Modem and your PCs or Network in your home, office, or hotel room and routes traffic between your Local Area Network (LAN) and the Internet through your ISP using what some call Internet Protocol (IP) or TCP/IP. The Internet protocol was not designed with the threat of hackers and viruses in mind, it was designed to deliver information, globally, efficiently and reliably. The primary function of the router is to facilitate this by routing only traffic that is meant for your eyes. There is quite a bit of junk that will fly by that's not important and you do not want that traffic on your LAN. The nature of a router, the firewall aspect of the typical router is the ability to disallow access. The complexity involved is dependant on the features, but even the most basic router will allow for you to communicate over the Internet while comfortably seated behind a locked door.
In reality it is several locked doors, 65535 doors actually, referred to as ports. Many ports have a commonly accepted use, such as web browsing (80 and 443), E-Mail (110 and 25), and inter-PC communication (135). This is NOT all of them, there are many more for many purposes. Most default configurations allow you to make outbound connections on all of these ports and will not interfere with your usage, some routers will allow adjustments of that but that's another discussion.
Your safety is found in the security of these closed doors. You should leave them closed unless you have a very specific need, such as a specialized software's need. This should be done only if you know exactly what you are doing and only for very specific ports. Some games require ports to be opened and directed to the PC playing the game, this is normally for hosting a game. Your router will have basic security restricting access to the configuration. suring configuration you should always change the password from the manufacturer's default. If you have purchased a wireless router, turn off the wireless if it not going to be used. Be very careful when configuring a wireless router, if you leave the wireless doors unlocked you leave access to your PC unlocked, but you also risk sharing your Internet connectivity with neighbours or passersby.
Routers are not expensive. Looking at the local Best Buy will snag you a router, a healthy safety plan, for less than $50. It is time to stop considering the value of a router and realize the necessity.