So, Apple seems to have stopped delivering security updates for Snow Leopard. I've been wondering for a while since then, what are the main risks users might now find themselves prone to? My primary machine is running Mavericks, but my old MacBook is still on 10.6, as is my parents' Mac Mini. Are there any big worries?
Realistically, if you have a good firewall, you are MOSTLY safe. Websites specifically designed to target your OS could exist though. You are at risk, but the level of risk is dependent on your usage. (Also, please have a firewall or you are at extreme risk). Antivirus tools will help after the fact.
Think of it this way (yay analogies)
Your computer is a home with windows and doors. Sometimes hackers can figure out how to unlock those doors and windows. The OS updates put new locks on them. Also close new ways hackers come in (like breaking the windows or cutting a hole through the ventilation). OS updates help block these methods as well. Without OS updates, you are left with only have the guard dog left (antivirus). While the dog can help here, some of them will kill the dog, some of them will be able to sneak past the dog.
Might as well install Sophos Antivirus too -- free enterprise-level AV that provides blocking for risky websites/website content. With this, using Firefox with NoScript as your browser, and having Little Snitch installed, you're pretty safe.
Just a heads-up, there's still lots of Mac malware being written that can affect 10.6; most is still using the 10.6 SDK or trojaned apps/exploits and bash scripts that'll run anywhere.
Oh, and disable any Java and Flash plugins in all your browsers -- this is still the major point of attack on Macs.