GameGenie, GameShark, Goldfinger, Pro/Action Replay..... I imagine I must have owned a cheat device for every console ever made. Most of the time they were for shits and giggles, but they proved to be real assets from time to time.
Like Amazingu said, the PSOne AR was crucial to get certain import titles to work properly on a modded system. Bust a Move 2: Dance Tengoku Mix, Vib Ribbon, and various Bemani titles were among some of the ones I remembered.
GameGenie for SNES was a savior when playing co-op titles like Contra III: The Alien Wars and Legend of the Mystical Ninja. 99 lives and infinite health gave my novice friends a leg-up when we were attempting to plow through the games together.
Short of visiting a DS Station download center in Japan, I think PAR was the only way to unlock the Elite Beat Agents in Ouendan 2.
I don't remember using the devices for RPGs much, but I did have a ball on my second playthrough of Final Fantasy X. Giving oneself a bountiful number of spheres meant opening up a whole new world of character customization on the Sphere Grid.
And, one of my favorite codes of all: opening up the four Shadaloo bosses for play in the original SNES Street Fighter II. (Yes, these were the days before Champion Edition.) It glitched like a bitch, but it was ridiculously awesome playing the likes of Claw and Dictator, albeit in an extremely limited capacity.