First, I would always be *incredibly* careful downloading so called "free files" from the 'net. More often than not, they are sites set up specifically to catch people looking for freebies and infect their systems with viruses, malware, and other malicious content (to steal your login info, to turn your computer into a 'bot to attack others, etc.)
Real free games are currently web-app only, and listed at Apple.com:
Game apps are currently only available with a jail-broken (hacked) iPhone, and then typically installed directly on the phone via something like Installer.app (you can Google iPhone jailbreak or search this site for details).
After February, real games will likely be available, but probably not for free, yet you'll get what you pay for -- a safe, secure, fun game that runs well on your iPhone.