Gran Turismo, MGS Peacewalker, the Monster Hunter series, God of War Chains of Olympus + Ghost of Sparta, the Patapon games, Death Jr., Motorstorm Arctic Edge, Dissidia 012 Duodecim, Twisted Metal Head-On, PixelJunk Monsters Deluxe, the LocoRoco games, the Fireteam Bravo games, Killzone Liberation, the Kingdom Hearts installments, Jeanne D'Arc, the Badman games, Valkyria Chronicles 2, Hot Shots Tennis Get a Grip.

The reason no one assembled a list is because it would be redundant. We could go back and forth title-for-title until the cows come home.

But being able to play ten or more year old games doesn't make something the best system ever.
Which is why functionality and original titles dominated the majority of my post, which I now lamentably wish you had enough respect for me to read. Peace Walker and Valkyria Chronicles II being head and shoulders above any title I've played in the longer time I've owned a DS Lite and GameBoy Color make the debate a subjective analysis that comes down to your preference and the games you've played. But the shockingly extensive list of most of the greatest games ever made is only the nitrous boost that makes the PSP far and away the best handheld ever made.