Well, then you can run .NET CF apps, since they're not processor-specific. (Upgrade to .NET CF 3.5 if you can though, so you'll have more apps to try.)
I was referring to the .NET CF runtimes specifically for programs written for the .NET Compact Framework, since those can run on any processor. Here's an example:
Though these were generally written for Pocket PCs, a lot of them will work fine (and often even in full screen) on core Windows CE 4 or later devices with the .NET CF runtime files installed.