yes you can.

stick your flash drive in the PS3, go to the games section on the XMB and then go to the one the shows your game saves (not the one with the installs)

so now you can highlight the game save you wish to copy, press triangle, select copy and then select the device.

LittleBigPlanet 1 and 2 do not have save files so you must load up the game, go to the option menu and select "Create Back Up Data"

Now go back to the XMB and you will see a save file that you can transfer to a flash drive. Make sure for each game you are copying the save data and the system data file.

On the XMB under settings, there is another way where you can back up or just move everything to another HDD.  I never used this feature though so im not sure if you can pick and choose items and if it lets you copy or if it forces you to move the data.