Kojima's idea of Metal Gear on the PS3, then taking it on the go on the NGP sounds pretty appealing...IF you don't have to buy a second copy. If they do something like DVD/Blu-Ray movies, where buying the game includes a digital/SD card copy of the game, that may work out - and keep gamers from buying games and spending money on other devices. (Makes sense, eh?)
Big difference maker is the dual analog, which was sorely lacking in the original PSP design. No sacrifice, unless the controls blow.
As Ship says, Lumines was definitely THE game for the PSP. It came out on release day and you couldn't put the thing down. Only much later did it see Xbox, etc. I'm sure Crisis Core fits the bill for many folks, too.
Wombat - seriously, a "must play" game = "your life would be empty if you never played it"? (So talkin' out of your ass! ;-) Give us ONE game that fits that definition. C'mon - you can do it!
Regarding the NGP, as jh6269 says: Playstation Suite. I also anticipate a lot of games being developed for the iPhone will find their way into a "mini" type of PSN store, we've also got cross-platform with Android, they'll have dual analog support in addition to touch screen, and be priced accordingly.
But will it sell? If it comes out around the holidays, has a strong suite of games, isn't priced too crazy and gets sufficient hype, it'll sell.