Stimothy, any downloads of PlayStation games that had been available for purchase in stores would be illegal, even those for the PS2 and PSP. The people providing them are doing so using files they "ripped" from the original discs. While it is legal to make a copy for "back up" purposes it isn't legal to make copies for the intent to make profit or any other way that could prevent a possible sale of the actual game. The PS2 system would also have to be modified to be able to play them.
As for the PSP, there are some games that would be considered legal as they are original creations- however, Sony isn't fond of the "homebrew" being made on the PSP and has been plugging the holes allowing this in the various firmware upgrades. As for other downloads such as the emulators for other game systems, the emulator itself may not be illegal but the ROMs (game files) are unless you own an original copy of the game. Hope this clears up some of the confusion a bit.