Don't worry sweets, I got ya covered! ;) I too am a big fan of monster breeding

Gameboy/GBC:

-Revelations the Demon Slayer

-Lil Monster

GBA:

-Shaman King Soaring Hawk/Sprinting Wolf (an ok game, but mostly a "rental")

DS:

-Digimon World DS

-Digimon World Dawn/Dusk

PS1:

-Jade Cocoon

-Dragon Seeds

-Monster Seed

-Eternal Eyes

-Digimon World 1, 2, & 3

PS2:

-Jade Cocoon 2

-Magic Pengel: The quest for color (a great game where you actually DRAW your monsters. Battle system is the same as DragonSeeds)

-Graffiti Kingdom (sequel to Magic Pengel)

PSP:

-Monster Kingdom: Jewel Summoner