Memory Stick Duo/Memory Stick PRO Duo
Both Memory Stick Duo and Memory Stick PRO Duo memory cards will work with the PSP 1000, 2000 and 3000 models. The Memory Stick PRO Duo is roughly half the thickness of the regular Memory Stick Duo, but shares compatibility and still fits the PSP's memory stick slot.
MagicGate Memory Stick Duo
The MagicGate Memory Stick Duo is discontinued, but will still work on your PSP. It incorporates Sony's MagicGate technology, which lets owners use content-protected media on any memory stick-compatible devices.
Memory Stick Micro M2
The PSPgo relies on a smaller memory stick than the other consoles in the PSP lineup. While incompatible with PSP models 1000 through 3000 without an adapter, the Memory Stick Micro M2 is 15 mm by 12.5 mm in size, and is less than half the thickness of the original Memory Stick PRO. Keep in mind that the PSPgo also has a built-in system memory, so you don't necessarily need a memory stick to save games and data to the console.
Third-Party Memory Sticks
Any memory sticks manufactured by a third-party will work on the Sony PSP provided they meet the memory stick format requirements (Duo, PRO Duo or in the case of the PSPgo, Micro M2) and sport the official Memory Stick insignia, which looks like a rounded "M" with three lines beneath it.