If you want to connect your iPod to your Xbox 360 and be able to play your music you are going to need to download the free Optional Media Update to play unprotected music (AAC format), which is the format that the iPod and Zune uses. I found this how-to which explains how to download it on the old dashboard. Here are the instructions on how to download the update on the New Xbox Experience dashboard.
1. Sign in to Xbox Live
2. Press the Xbox Guide Button (the big silver X button in the center of the controller)
3. Go to Marketplace
4. Select Game Marketplace
5. Scroll down and select All Games
6. Select the letter "O"
7. Download the Optional Media Update (4.64 MB as the time of this writing)
As of this writing you can't play music or video from your iPod Touch or iPhone, but you can see pictures. The reason is because the iPod and iPhone use a different path than the previous generation of iPods.