In Final Fantasy IX the summons are called Eidolons. There are 2 characters that can summon Eidolons: Garnet (Dagger) and Eiko. The attacks of the Eidolons are mostly the same as from the GFs in FF8 and Summons in FF7.

.: Garnet's Eidolons :.

Name: Shiva
Attack: Diamond Dust (Ice)
Item needed to learn it: Opal
AP needed to learn it: 20
Used MP: 24

Name: Ifrit
Attack: Hell Fire (Fire)
Item needed to learn it: Topaz
AP needed to learn it: 20
Used MP: 26

Name: Ramuh
Attack: (Thunder)
Item needed to learn it: Peridot
AP needed to learn it: 20
Used MP: 22

Name: Atomos
Attack: (Gravity)
Item needed to learn it: Amethyst
AP needed to learn it: 25
Used MP: 32

Name: Odin
Attack: (Instant Death)
Item needed to learn it: Dark Matter
AP needed to learn it: 30
Used MP: 28

Name: Leviathan
Attack: Tsunami (Water)
Item needed to learn it: Aquamarine
AP needed to learn it: 40
Used MP: 42

Name: Bahamut
Attack: (Non-Elemental)
Item needed to learn it: Garnet
AP needed to learn it: 80
Used MP: 56

Name: Ark
Attack: (Dark Elemental)
Item needed to learn it: Pumice
AP needed to learn it: 100
Used MP: 80

.: Eiko's Eidolons :.

Name: Carbuncle
Attack: (Reflect, Haste,
Shell, or Vanish)
Item needed to learn it: Ruby
AP needed to learn it: 35
Used MP: 24

Name: Fenrir
Attack: Earth or Wind
Item needed to learn it: Sapphire
AP needed to learn it: 30
Used MP: 30

Name: Phoenix
Attack: (Fire at enemies/Revive allies)
Item needed to learn it: Phoenix Pinion
AP needed to learn it: 40
Used MP: 32

Name: Madeen
Attack: (Holy)
Item needed to learn it: Ribbon
AP needed to learn it: 120
Used MP: 54