Now that we have finished with the PS3, I'm still trying to decide whether to split up PSP and Vita or to do it all as one. I'll leave that in your hands. Let me know if you think they should be split up. :) 

As far as my favorite PSP games, my favorite ones were Daxter, God of War: Chains of Olympus, God of War: Ghost of Sparta, R&C Size Matters, Secret Agent Clank, Mega Man Maverick Hunter X, Crisis Core: FFVII, Lumines, FF Tactics, Disgaea, LocoRoco 2, and Patapon 2. Shoutout to Lego Indiana Jones because I feel like somewhere the ghost of my PSP is still trying to load the next level. 

If we do combine consoles, I'll say LBP Vita, Rayman Origins, Persona 4 Golden, Disgaea, Uncharted: Golden Abyss, Motorstorm RC, and Sly Cooper collection into the fray....

PSP

A lot of great games of different genres and series.

FFVII Crisis Core
Kingdom Hearts Birth By Sleep
FF Dissidia games
Ridge Racer 1 and 2
Wipeout Pure
Darkstalkers Chronicle Chaos Tower
Megaman Powered Up
Megaman Maverick Hunter X
GTA Liberty City Stories and Vice City Stories
God of War Chains of Olympus and Ghost of Sparta
Final Fantasy I Anniversary
Final Fantasy II Anniversary
Final Fantasy IV Complete Collection
Breath of Fire III
Disgaea Afternoon of Darkness
Disgaea 2 Dark Hero Days
Jeanne D' Arc
Persona 1 Portable
Persona 2 Innocent Sin
Persona 3 Portable
Star Ocean First Departure
Star Ocean Second Evolution
Tales of Eternia
Tekken Dark Resurrection
Tekken 6


So many great games , moreso that I havent listed.

Mega Man Powered Up
Mega Man Maverick Hunter X
Ultimate Ghosts`n Goblins
Harvey Birdman: Attorney At Law

All for the PSP

Macross Scramble Delta

Pata-Pata-Pata-Pon

Pursuit Force 1 and 2. Very hard, especially the first one, but addicting as hell.

Killzone Mercenerys

Metal Gear Solid: Peace Walker is my personal favorite. But there's several others that definitely come close.

Wipeout Pure
Both God of War PSP games (Chains of Olympus and Ghost of Sparta)
Resistance: Retribution
Daxter

I never had a PS Vita though. 

Persona 4 Golden is my favorite Playstation Portable game and my Top 1 Game Ever

Is this getting a poll?