For depictions of Satan specific to the Megami Tensei franchise, see this page instead.
Satan, which means "the Accuser", is the primary antagonist of the faithful in Abrahamic religions.
In the Hebrew Tanakh, what Christians refer to as the Old Testament, Satan's role is that of a judge of mankind. He is not a fallen angel (though verses in Ezekiel hint at this) but one of the heavenly host who, true to his name, acts as an accuser, akin to a prosecutor in a courtroom today. In apocryphal Jewish texts such as the book of Enoch, Satan did indeed fall from heaven for being jealous of God's creation of Adam and Eve.
In Christianity he rules over hell, overcoming his temptation is the goal of believers and his defeat will signal the coming of paradise. In Islam, he is referred to as Iblis or Shaitan.
In Video Games
Satan made an appropriately metal appearance as " Lou", for the final boss battle in Guitar Hero III: Legends of Rock. He is also featured in the "storyline" of the career mode for Guitar Hero III. He first appears as the agent that signs the player's band to a label, and also frees their band from prison, taking them on a whirlwind tour. Eventually, when the player is famous enough, their character tells Lou that they don't need him anymore. It's at this point that he turns out to be Satan himself, and challenges the player to a guitar duel for their soul!
The Binding of Isaac
In the PC game The Binding of Isaac Satan appears randomly offering items to Isaac, including "The Pact", a presumable deal with the devil that turns his skin black, but grants him greater abilities in combat. Satan also appears as a two-part boss monster in the content added in the Halloween update to the game. If the player attempts to use the Bible on him they will be killed instantly.
Sam & Max
In the Sam & Max games Satan appears as a very comical figure. Instead of being a mythological environment of fire and brimstone hell appears as an average company office and instead of appearing as an evil overlord, Satan appears as a rather average office manager.