The appropriately named PSX4iPhone homebrew application allows you to enjoy classic PlayStation games from the comfort of your Apple iPhone. As with any emulator software, PSX4iPhone — in and of itself — is not illegal. However, the means by which you acquire PlayStation (PSX, PSone, PS1, whatever you want to call it) ROMs may tread on a legally gray area.
That said, this is a great advancement for the Apple iPhone, because the best emulator created thus far has only been for the original 8-bit Nintendo (NES). By moving onto the 32-bit PlayStation, developers have leapfrogged the 16-bit generation altogether. I’d imagine that the components found within the iPhone are perfectly capable of handling most of the basic PSX games; in fact, they say that it “may be compatible with approximately 75 percent” of the library.
Credit for the PSX4iPhone application can be given to a coder called zodttd. The app should work with both the iPhone and the iPod Touch. Beyond basic emulation, the app also offers enhanced screen scaling, screen placement, and game save options. More information here.