Apollo is the name of a couple of characters in the Battlestar Galactica universe:
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Original Continuity
Apollo is the son of Commander Adama & Ila. He is played by Richard Hatch (who also portrays Tom Zarek in the new Battlestar Galactica). Apollo has a sister Athena, also a Warrior, and a brother Zac who was killed in a Cylon ambush prior to their attack on the 12 colonies. Apollo's mother was killed in the attack on the colonies.
New Continuity
In the new Battlestar Galactica (re-imagining), Apollo is no longer the character's name but rather his call sign (although Laura Roslin calls him 'Captain Apollo' anyway, as "it has a nice ring to it"). His real name is Lee Adama and he is played by the actor Jamie Bamber.
Also in Battlestar Galactica (re-imagining), Apollo is the name of one of the Lords of Kobol (one of the Colonials' gods). Apollo is the son of Zeus, and Lord of the Hunt and Lord of Healing.
Lord Apollo is symbolized by the Arrow of Apollo, a religious artifact brought from Caprica to Kobol.