StyleTap, which costs US$49.95, is a Palm OS emulator that allows users to run Palm OS 5.2 or earlier apps on Android or iOS; it also supports Palm OS apps that run on native ARM code. If you want to run StyleTap on Android you will need an Android 2.0 or higher device. If you want to run StyleTap on iOS, you will need a jailbroken iPhone, iPod Touch, or iPad running iOS 3, 4, or 5.
StyleTap for Android and iOS does have some limitations, such as Bluetooth not being supported for Palm apps running on Android, and there are semi-detailed instructions you need to read to learn how to use StyleTap. However, if you insist on legacy Palm apps on new hardware, StyleTap may just be worth your $50. (Be sure to download the 14-day trial before shelling out money so as to test the software.)