Phoenix

A bird composed of fire who revives all dead/knocked-out allies and sometimes gives a fire attack as well. In FF5, the Phoenix was Lenna's Dragon who killed itself, then rose to become Phoenix. Usually it can be summoned at will, but in FF8, Phoenix could only be called using Phoenix Pinions. Once this item was used, Phoenix appeared randomly if all playable characters were knocked-out in battle.

FF5 in-gameFF5
-Phoenix
ATK: not named
FF6 in-game FF6 Locke resurrection sceneFF6
-Phoenix
ATK: Rebirth
FF7 in-gameFF7
-Phoenix
ATK: Phoenix Flame
FF8 in-gameFF8
-Phoenix
ATK: Rebirth Flame
FF9 in-game FF9 in-gameFF9
-Phoenix
ATK: Rebirth Flame
FF12 Clan PrimerFF12
-Phoenix (boss)

It's not a summon, but a boss. However, since it's part of four bosses representing the four Chinese God-Beasts (Gen-Bu, Seiryu, Byak-ko and Suzaku) it's probably more meant to be Suzaku than the more Western Phoenix.
CP: Being a legendary Avion said to have been tasked with the Protection of the southern Lands by the Gods themselves. Its Body is covered in Feathers of rich Amber, and its Head is adorned with elegant Horns. Called the Firebird for the way it flames when climbing into the Sky, and revered as an Anima of the Sun.
TA in-gameTactics Advance
-Phoenix
ATK: Not named
FFU FFU FFU Giga-PhoenixUnlimited
-Phoenix / Giga-Phoenix
SOIL: Mother Black + Fire Red + Burning Gold