Browse the Web
Most websites work on the PS3's browser so you shouldn't run into too many compatibility issues. You can check your email, update social networking sites and browse all your favorite websites on your TV using your PlayStation 3.
Play Games
There are many free games available online. While some may only work with an actual keyboard, you'll be able to play some with your PS3 controller. With Adobe Flash enabled in the Internet browser by default, the PS3 is fully capable of running flash games on websites such as MiniClip.com (see resources). Many of the free flash games offered online are similar to the ones available for purchase on the PlayStation Network, which could potentially save you money if you stick to the free stuff.
Watch Videos
With the addition of Flash Player 9 now included with the PS3's Internet browser, you are now fully capable of watching flash videos on the Internet. Many sites offer free flash videos and you can even watch some network television shows on TV network websites. While you can just as easily do this on the computer, doing so on the PS3 makes it easier to watch these videos from your television. One downside, though, is that as of early 2010 Hulu.com, a huge supplier of free television shows and other flash videos, no longer works on the PS3. Despite the lack of Hulu, there are still plenty of sources for legally watching free videos online.
Connect with Friends
Certain websites, such as eBuddy.com, offer online instant messaging from their website. Some sites offer unique instant messaging clients designed specifically for their site but many offer the ability to import buddy lists from and chat with people on Yahoo!, MSN and AOL instant messenger services. As long as you have a keyboard, this could be a great way of chatting with friends while you're using your PS3's Internet browser.