Original Devilman TV anime was actually concived of FIRST by Go Nagai, who wanted to do an anime with an anti-hero of sorts with demons. The manga is a completely different story.
In the TV anime, Akira is killed by Devilman (not called Amon, just "Devilman", that's his name) along with his father at the very start of the series. Devilman posesses Akira and intends to pose as him, having orders to destroy human civilization. After a short ammount of time Zenon (demon's leader in this version, there is no Satan) realizes that the humans are still around and sends a demon (demons in this series don't posess humans, they just go around and fuck shit up) to investigate. Devilman is found living life as Akira Fudo and not destroying humanity because he's fallen in love with Miki, and destroying humanity would probably hurt his chances with her. The most he's done against humanity is beat up kids at school (seriously, Devilman beats up people who are just mostly minding their own business, he's a bully, although Miki usually gets him to stop by hitting him) and breaking various traffic laws on his motorcycle. Devilman turns into his devil form then gets giant to fight the demon, and kills it. The rest of the series follows a monster of the week format, with Devilman fighting and killing some demon or another in each episode. At the end, Miki finds out that Devilman is a demon, but since he's protecting her she still loves him. After that it basically goes on to say that Devilman would fight more demons as Zenon would keep sending them after him, but the series ends there.
Really, it was actually pretty good. It had a large influence on later action anime and was one of the first of it's kind.