These are all the Summon Materia in the game. Listed is the name of the materia( in alphabetical order), the name of the summon it causes, its type, and where you can find it.
ALEXANDER-Holy Judgement-Holy-Find Ice Gate( see hints and tricks)
BAHAMUT-Mega Flare-Type less-Beat the Red Dragon in the Temple of the Ancients
BAHAMUT NEO-Giga Flare-Type less-Whirlwind Maze
BAHAMUT ZERO-Tera Flare-Type less-Recieve from the Huge Materia in Cosmo Canyon if you have the other two Bahamuts
CHOCO/MOG-Deathblow/Fat Chocobo-Type less-In your first visit to the Chocobo Ranch talk to the chocbo near the fence and say WARK!! Note this materia sometimes causes stop
HADES-Black Claudron-Alter Status-In the sunken plane( Gelenki)
IFREET-Hellfire-Fire-Jenova Birth
KNIGHTS OF THE ROUND-Ultimate End-Type less-NE Island Materia cave. You need a Gold Chocobo( see chocobo breeding section) see map
KUJATA-Tri Disaster-Fire/Ice/Lightning/Earth-Sleeping Forest it's the little red ball that runs around
LEVIATHAN-Tidal Wave-Water-Beat the Wutai Pagoda and Godo will give this to you
ODIN-Steel Bladed Sword/Gungnir-Holy-Open the safe in the Shinra Mansion( see getting Vincent in hints and tricks).
PHOENIX-Phoenix Flames-Fire/Holy-Condor Fort defeat the Shinra Army in the search for the Huge Materia
RAMU-Judgement Bolt-Lightning-Gold Saucer Chocobo Racing find this when you have to race for your freedom
SHIVA-Diamond Dust-Ice-Lower Junon save Priscilla and this is your reward
TITAN-Earth's Anger-Earth-Gongaga check the reactor after Scarlet comes
TUPON-Disintegration-Wind-Frog Forest