Safe is perhaps too all inclusive a term. It is generally safe to run OS X apps because there is so little malware in existence. But it is a good habit to be careful. If you would prefer to be careful, here are some things to consider...
If you install a program and it doesn't ask for admin privileges, it is safe-er than one that does. However any executable on Unix has the potential to contain malware and there are known techniques for Unix executables to obtain root access when run as a normal user. Happily there isn't much malware out that targets Linux or OS X right now, but I wouldn't download and run anything from those "link farm" sites that somehow manage to plant themselves near the top of google page rank yet do not contain original content, only links to original content. The best place to get OS X apps was recently taken down by apple but will soon be replaced by the OS X app store. Another good source is MacUpdate. I would avoid sites that don't "look quite right" and use Mroogle to search MacRumors before you trust and run OS X software you never heard of before. This is why OS X asks you each and every time you download and run something you never ran before!
Another thing to avoid is being the middle man who spreads windows malware. Never forward a message containing executable content, even if that content is a windows exe file. Your friends might assume it's safe 'cuz they assume you use a Mac and can't spread windows malware but that doesn't mean you cant unknowingly spread it by unthinkingly forwarding email that contains it. There are a number of companies that sell OSX virus scanners which detect the handful of OS X exploits and scan for windows malware to help prevent you from unknowingly spreading it. This is overkill. If you take your time and are careful, it is fairly easy to avoid forwarding windows malware (attachments) to your friends. Extensions to watch out for are .exe, .wsh, and of course sneaky variants like .txt.exe and so forth.
