While it's not 100% clear via the wording on the PSN blog, the statement that Nick Caplan of Sony Europe made to Kotaku's reporters is clearer.
If you have a PS3 and a PSP it's a total of four free games.
"Sony Computer Entertainment Europe's head of communications Nick Caplan writes today that PSN users will get up to four free games for the PS3 and PSP from a select list. PlayStation Network account holders will be able to claim them from the PlayStation Store when that goes live—"just a little while longer," Caplan writes—provided they have access to the Store in their country."