Original Continuity

Apollo is the son of Commander Adama & Ila. He is played by Richard Hatch

Richard Hatch (actor)

Richard Hatch is an American actor. He is best known for his role as Captain Apollo in the original Battlestar Galactica television series, and also as Tom Zarek in the remake of Battlestar Galactica....

 who also portrays Tom Zarek

Tom Zarek

Thomas "Tom" Zarek is the name of a fictional character on the Syfy series Battlestar Galactica. He is played by Richard Hatch, who had previously portrayed Captain Apollo, a character on the original Battlestar Galactica series of the late 1970s....

 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 current incarnation, Battlestar Galactica (re-imagining), Apollo is no longer the character's name but rather his call sign (although Laura Roslin

Laura Roslin

Her first actions include organizing all FTL-capable ships together and convincing Commander William Adama to abandon a retaliatory attack on the Cylons. President Roslin and Billy Keikeya, her aide/press secretary/chief of staff, establish a working office space aboard her transport, renamed...

 calls him 'Captain Apollo' anyway, as "it has a nice ring to it"). His real name is Lee Adama

Lee Adama

Leland Joseph "Lee" Adama is a fictional character in the television series Battlestar Galactica. He is portrayed by actor Jamie Bamber. He is one of the main characters in the series.-Early life:...

 and he is played by the actor Jamie Bamber

Jamie Bamber

Jamie Bamber is the stage name of Jamie St. John Bamber Griffith , a British actor known most widely for his roles as Lee Adama on Battlestar Galactica and Detective Sergeant Matt Devlin on the ITV series Law & Order: UK...

.
Also in Battlestar Galactica (re-imagining), Apollo is the name of one of the Lords of Kobol

Lords of Kobol

The Lords of Kobol are deities featured in the fictional universe of Battlestar Galactica. The Lords of Kobol are worshiped by the humans of the Twelve Colonies...

 (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 Kobol to the Colonies.