Mods: Maybe you should make this thread or another one similar to this sticky since this question seems to be asked a lot about all Macs.
Mackson, Robbie is right, the iMac has no built in video adapters, so you will need to purchase an external box. However, he there is a device that he may not be familiar with that will allow you to play video game consoles. But first, let me summarize your choices:
EyeTV 200 or Formac Studio TVR
While the EyeTV 200 is the better choice, both are fairly similar. They both allow you to watch TV on your mac. They hook up to your Mac via Firewire and have a built in MPEG-2 converter--perfect for digitizing old video tapes. The problem with these devices is that because they have this converter, there is a slight delay. This makes playing any sort of video game impossible. For don't be too upset, there is another solution...
EyeTV EZ
I originally purchased the Formac, but was upset when it didn't play video games. I emailed Elgato, makers of the EyeTV line, to find out if they had any solutions. They did. The EyeTV EZ (about $150, available at elgato.com) is a fantastic device. It too allows you to watch and record TV. The quality of the recordings is no where near as good as on the Formac or the EyeTV 200, but there is a huge advantage. The EyeTV EZ hooks up via USB and has no built-in converter. Without a converter, there is no delay, allowing you to play video games on your iMac perfecly.
Ultimately, if you want to play video games, buy an EyeTV EZ. If you want to watch TV, an EyeTV EZ is probably the best choice as well. But if you want to convert VHS tapes or turn your iMac into a TiVo, buy an EyeTV 200. I would recommend a Formac, but unfortunately, their customer support is terrible and their software pales in comparison to EyeTV.
Hope this helps.