For PSP, ill just get this out of the way:
Wipeout Pure
Sure, Tekken Dark Res just came out. Its mind-blowing, pretty, amazing its on a portable. OMG Valkyrie Profile on psp, that too is awesome. However there hasnt been a PSP released that is as technically impressive, and feature packed as Wipeout Pure. Just the number of downloadable tracks alone is staggering. The game runs at a solid framerate and offers some of the most beautiful visuals available on a portable. Gameplay wise its a ingenious mix of Wipeout XL and Wipeout Fusion.
Now at Greatest Hits status, you can get Wipeout Pure for 20 bux. Not owning this is like slapping Jesus in the face.
And for DS, tough call:
Phoenix Wright is neat, but a lot of it is trial (lolz) and error. Sometimes it feels like im groping around in the dark with some cases. New Super Mario Brothers is awesome, but I think lacks lasting challenge.

Then there's Advance Wars Dual Strike. I own the first two, and ill say that I understand why a few people were turned off by this installment.
Until mission 10, it is Advance Wars 2. None of he new stuff is incorperated. No doubt they felt as the first entry to the DS library, that there was a greater chance many would come ino the series new, and need some tutorial. In fact I think DS has more 'tutorial' than the first Advance Wars. This complaint is valid.
BUT, once past mission 10 you wil be faced with some of the toughest fights. The double CO battle system and use of dual screen (while not often enough for me) will have you on the ropes digging deep into your bag-o-strategy to find a winning solution eary on. Once practiced you'll be tht much better! COME ON! BUY IT!
However hating on the headphone wearing street talking CO is inexcusable. He is hilarious.