Saving your game in the original PlayStation version of "Crash Bandicoot" was poorly explained and often frustrating. After making the move to the PS3 as a PSN download, the process remains annoyingly convoluted. In addition to having to track down certain bonus stages just to save, you also have to create a virtual memory card to actually store the save.
Virtual Memory Cards
Go to the Game menu on the PS3's home screen and select "Memory Card Utility (PS/PS2)." Select "New Internal Memory Card," followed by "Internal Memory Card (PS)." You can assign the memory card a name for easy identification or leave it as is, but when you select "OK" the card will be created. If no card is assigned to a virtual card slot, you will be prompted to assign the card to "Slot 1;" do so. Once the card is assigned to a slot, it should be ready to save your "Crash Bandicoot" and other PS1 game data.
Actually saving your "Crash Bandicoot" progress requires you to access one of the three bonus stages in the game. Bonus stages are accessed by finding character tokens throughout a level and getting all three of a certain type. "Tawna" tokens look like a 2D image of Tawna, a blonde female bandicoot. They lead to a simple bonus level. At the end there is a portal near Tawna that will enable you to save; it also provides a password to enter if the save file doesn't work. These tokens can be found in 15 of the game's levels, with at least one set on each island. "Cortex" tokens look like a 2D image of Neo Cortex, the game's villain. They are found in only two levels: Sunset Vista and Jaws of Darkness. Cortex bonus stages feature considerable challenges and only save at the end of the stage; they also unlock hidden stages on their maps. Links in the Resources section detail where to find these tokens.