There have been a lot of questions online, especially on Yahoo Answers about whether you can buy iPod games with an iTunes gift card. Before I answer the question, I want to make a distinction between the iTunes gift card and the Apple Store gift card. The iTunes gift card can be used to purchase stuff you can play or use on your iPod-like devices (iPod Classic, iPod Nano, iPod Touch, and iPhone). The Apple Store gift card can be used to purchase hardware and software at the Apple Store (like the iMac, MacBook etc). They are not interchangeable. For example, you cannot use the iTunes gift card to purchase an iMac, neither can you use the Apple Store gift card to purchase music at the iTunes Store.

So, back to the question of whether you can use the iTunes gift card to purchase games. The answer is a qualified yes. You can use the iTunes gift card to purchase games that are compatible with iPod-like devices (iPod Classic, iPod Nano, iPod Touch, and iPhone). Some of these games are built exclusively for specific devices. For example, there are games designed for the iPod Nano that cannot be played on the iPhone. In addition, these games cannot be played on your computer.
To buy iPod games, simply log-on to your iTunes, go to the iTunes Store and click on iPod games.
Apart from iPod games and music, you can also use the iTunes gift card to buy Podcasts, TV Shows, Music Videos, Movies, Audiobooks, and applications designed for iPod like devices.

Update (01/30/2009)
In response to some of the comments below, I called iTunes support today asking them to walk me through the steps of buying an iPod game with an iTunes gift card. Below is what they told me.
1. First, you need to have already redeemed your iTunes gift card. Meaning that your iTunes account should show your iTunes gift card balance. For steps on how to redeem your iTunes gift card, click here.
2. Once your account is showing the gift card balance, click on “Ipod Games” under “iTunes STORE”. Select the game you want, and click on “Buy Game”. The price of the game will then be deducted from your gift card balance.
As long as there is a balance on the gift card, I am told that it will be the default payment method, until the balance runs out, at which point it will go to the credit card or ask for a credit card. If you have not yet redeemed your gift card, the system will NOT prompt you for a gift card (it will default to a credit card in absense of a gift card balance).
3. Once you purchase the game, you now need to sync the game to your iPod. For instructions on how to do that, click here.
Hope this helps.