Here are some tips to keep yourself protected.
1.) Use a router for any internet connection (other than dialup). Be sure to keep updated the firmware on your router to the latest from the manufacturer. A router uses something called NAT (Network Address Translation) that works fairly similar to a firewall - however this is more like a firewall. NAT in most cases will not allow ports to be scanned & forwarded behind it. Also, the router will be your external IP address leaving your computer on an internal IP address. If ports on your router are not forwarded to your internal IP addresses (usually 192.168.*.* type of address) then a hacker on the internet will have a lot of difficulty scanning your computer. They will merely scan a router which in most cases is rather "stupid" and very hard to attack.
2.) Keep your operating system updated. For Windows, Mac, Linux, and Unix users, always install the latest updates.
3.) A soft firewall is always recommended. This would be considered a firewall on the system you use. This is where you computer is basically asking you permission to install certain pieces of software along with asking if you want to allow certain connections on your computer. Again, a router will help you avoid a ton of mischief from hackers. This is more or less fail safe.
4.) Make all of your passwords HARD, with letters, numbers and symbols. Make them at least 20 characters long. Do not include the names of your kids, dogs. Never make them just common words. A good example would be: MrTsayshackersarefools33@3
5.) If you run a wireless network, always use WPA or WPA2 security. Again, make your password at least 20 characters including letters, numbers, and symbols. DO NOT SKIMP on wifi passwords.
6.) Install a good virus scanner and spyware scanner if running any type of Windows. It is also wise to install virus and spyware scanners on Macs. Linux and Unix systems typically do not get spyware or viruses. Remember, a virus/spyware scanner will do you NO good if you do not update it frequently. Viruses and spyware are literally released daily.
7.) Using web access email is always the safest. Free email accounts such as Yahoo, Gmail, or Hotmail always keep high levels of security on their sites. Also, always be very weary of any email you get that tells you to click links (Paypal for example). Hackers can make very good copies of websites like Paypal (including logos & design) and spam you. You click thinking you are at Paypal, put in your user name and password, and the hacker then has your user name & password. If you get an email from sources like your bank account, Paypal, Ebay etc., open a clean browser go directly to the site, and log in.