Before looking for games, you need to make a few decisions:
1) Are you looking for free games or are you willing to pay for them?
2) Do you want a game that can be downloaded to your iPhone or are you happy to play online games?
3) Are you waiting for a full console game or are you happy with the usual type of games that are available for mobile phones?
There are free games available for iPhone, but most of them are played online. In other words, it doesn’t download them to your iphone.
Playing games online means having free games, also if you know where to look, you can have a good variety of games to choose from and there are some games where you can compete against other players.
Downloading games to your iPhone means that you can play them anytime, even if you don’t have internet access. But they take memory!
While there are some great free games available, it can be quite tedious to find them on the internet, as there are many spammy sites that need to be checked before good game sites can be found. Some sites specialize in finding them for us and I recommend that you keep some of these bookmarked and keep checking their latest updates.
If you want to download games to your iPhone, you have the option of purchasing them through Apple (simple and easy to find) or through a membership site (these sites are not always easy to find, but much cheaper).
If you want “full console” type games, then you really have to pay, in the short term, for these types of games. They are still a few months away, and membership sites may have them available by then, which will save you considerable money. So I recommend that you check them out before spending a small fortune on iTunes!