Some iPhones and iPod Touches running an older version of iOS have been unable to directly download apps from Apple's app store for a few days now. The issue appears to have resulted from a server-side update from Apple that has broken the ability for a device running iOS 3.1.3 and earlier to download new apps, although updates still work and apps downloaded via iTunes can still be synced over from the desktop. There are several other issues with the App Store on these devices, including missing thumbnails and poorly-rendered pages.
Apple's support forums has several threads discussing and confirming the issue, though it's not clear yet if it's a universal issue or only affecting a certain subset of users. It's especially problematic because iOS 3.1.3 is the final version released to the original iPhone 2G and the first-generation iPod Touch, meaning those devices are unable to directly download and install new apps.
Since it was apparently a recent change on Apple's servers that broke App Store downloads for these older iOS devices, hopefully the same sort of change can bring them back, and soon.
Update: Forum users are now reporting that Apple has fixed the issue.