Sony's Jack Tretton warmed up the Sony PSP with HDD rumor that is 3 years old at the E3 2008.

Sony highlights the fact that you can use downloaded movies from the new Playstation Store Video shop also on the PSP. This of course requires storage on the PSP.
The largest Memory stick you can get right now is 16GB and sells for $148 on Amazon.com.

An internal memory of a future Sony PSP would need to at least have that much capacity. Asus sells the Asus Eee PC 1000 with a 40GB SSD. This could also be an option for a future PSP, especially as SSD prices are coming down right now.

I do not see a hard-drive making any sense. Movable parts are just not good to have in a portable device.

Photo:
Sony PSP Gadget Model Megan.