Made popular in the animated series for his pursuit of the Lazarus Pit, which can greatly extend his life, or even bring him back from the dead.
In the video game adaptation of Batman Begins Ra's Al Ghul appears not as the nigh-immortal character from the comics, but instead as ninja Liam Neeson like in the movie. Liam Neeson even provided his voice and likeness for the game. Instead of being the leader of the League of Assassins (like in the comics), he is the leader of the League of Shadows. The name change was likely because Bruce Wayne wouldn't have even considered joining the organization if he knew it was filled with assassins.
Batman: Arkham Asylum
Ra's Al Ghul has a rather lifeless role in Arkham Asylum. Literally, because he is dead in the game, and appears in a body bag. Scanning him is the way to solve one of The Riddler's riddles in the game.
Batman: Arkham City
Ra's has a much larger role in Arkham City, if only because he was brought back to life by a Lazarus Pit. In the game he is leading the League of Assassins along with his daughter Talia.
Batman: Arkham Knight
Ra's is the main antagonist of the "Shadow War" side mission of the Season of Infamy DLC pack. He is put on life support by a group of League of Assassins loyalists. There are two endings to his mission. Ra's either gets resurrected with Nyssa dying or he gets put off life support and sent to GCPD.