The show was originally supposed to run for five seasons, so the official story arc only covered those seasons. This is important as many fans speculate that God was in fact Chuck Shurley, the "prophet" from Season 5. Strong evidence of this theory (including the actor himself confirming it) can be found here and in the video:
Whilst this is certainly not definitive, it's fascinating. If Chuck was God, then they'd either need to bring the actor back or cast a new God. The former would be more likely, but ultimately neither is particularly needed. The show has dealt with heavy themes since Season 5, but nothing approaching the apocalypse or Lucifer Rising - meaning if God wasn't going to intervene then, it seems very unlikely (canon-wise) he would intervene now.
Ultimately though, though, God plays no role in the show after Season 5. We hear him being discussed and his apparent abandonment of Heaven used as a reason for the many revolts and rebellions that are being fought, from Raphael trying to seize control, to Castiel trying to become more powerful, to Naomi trying to reestablish control, to Metatron creating the Great Fall. The closest explanation we get is from Castiel, in the episode Road Trip, where he discusses the angel Gadreel, who allowed Lucifer into the Garden of Eden. Castiel says:
CASTIEL It's his fault -- all of it. The corruption of man, demons,
hell. God left because of him. The archangels -- the apocalypse. If he
hadn't been so weak, none of it would have happened.
In short - God is very much AWOL. He may or may not appear in the series (it hasn't been confirmed) or indeed, he may have already appeared if you believe the Chuck Shurley theories.