What do you think makes the PERFECT villain in a good roleplay?

I don't know about the explaining the death trap part. It seems like something you'd get from The Riddler, and he was just a narcisist.

Compromise...How about a sophisticated psychopath?...No, that wouldn't really work, would it?
 
Backstory for villains really depends on how deep you want to go with them. I mean a crazed villain who enjoys killing actually might do better with no background like The Joker from batman. Then there are villains who really have no need for their background but are still cool anyway.

One good example of this specific type of villain is Kyouji Mujo from S-Cry-Ed. He had the same creepiness and overwhelming confidence Shinigami had. (Although he displayed it in a much more cocky attitude) but he barely had any background. The only thing you got from him was that he entered "The Other Side" once but he was still a brutal villain that again you loved to hate.

As for villains with backgrounds, they usually have them to make them seem more sympathetic to show how they got into this crazy state of mind. Shinigami kind of used this but it was much less sympathetic rather than explaining why he needed to do what he did and what reason he wants to come back for. This next bit is a bit of spoiler so if you want to read iCSYL but haven't gotten to the end I'll hide it from you.

Shinigami's role in the ICSYL series was to recomplete himself. Being seperated had scattered his power and with it his intentions. He planned on coming back to life and picking up where he left off which was, simply put, an interdimensional war that had come to a halt in Shintaion. At the peak of his previous regime he managed to destroy countless worlds and in more than just the physical sense. He depleted the elements of each world as he fought making them just a hollow shell. This villain was supposed to be portrayed as the epitome of power and malice but at the same time forced to work with someone to come back.

His intentions were somewhat revealed bit by bit but the grand picture of events never really was explained until the start of the final sequence of fights with him. And in about two or three paragraphs worth he explained away nearly everything that happened in the whole damn series XD.

I guess what I eventually ended up talking about is what else makes a villain good. A villain, in some rare occasions, should be able to make the hero feel like a helpless cog in the grand machine he has constructed.