I've been on the Internet for about ten years now, and I've developed fairly good instincts about what's safe and what's not. For instance, chat rooms are very dangerous. Not because the nubile 14-year-old girl you're attempting to woo is in fact a grizzled undercover cop named "Al." No, the true hazard is that you might accidentally encounter a 14-year-old girl:
OMG! OMG! R U 4 reel!!!! :):):)
Et cetera. So my advice is to skip chat rooms.
I rarely recommend downloads, at least not of popular stuff. Screensavers, icons and wallpapers from commercial sites are often buggy with spy-and-adware.* One study found that 80% of sports screensavers from one site were infested with it.
One exception I'll make is when it comes from a site identified with one person, who puts, in effect, her personal guarantee on the program's integrity. Such would be AJScreenSaver. It's a very nice collection of 14 different clock designs, such as the one pictured, designed by Charles Salim.
You can get many more safe, free screensavers here. (Note: Only the screensavers on the site itself are screened for viruses, spyware, etc. They can't vouch for any programs appearing in banner ads.)
*If you're not clear on what spyware is, this Wikipedia article should get you up to speed. Spyware isn't inherently destructive, though it can drain your system resources and slow your computer down if you have too much of it running.
It's a good idea to periodically scan your computer. Two of the best freeware programs to check for it are Ad-Aware (download Ad-Aware Personal from the left sidebar or from here) and SpyBot.
Some file-exchange programs like Kazaa and Limewire won't function if you remove their included spyware. You can quarantine individual spyware components until you determine they aren't needed for other software to work, at which time you can remove them entirely.