Some game are compatible with the new xbox 360. They are called backwards compatible and you do need to flash upgrade the OS on the new xbox 360 system.
You need to go to the xbox website and go to support and download the flash update then burn it to disk and put it on the xbox to update the software. Again not all old games are compatible with the new xbox system. If your buying used games like I do make sure it says bc next to the title before buying them.
Here is the link to the upgradehttp://www.xbox.com/en-US/games/backwardscompatibility.htm