Nowhere has this trend been stronger than in the most popular RPG of all, Dungeons and Dragons. In 2nd edition, there were many campaign worlds that included random tables in character creation. Darksun gave everyone random psionic powers. Birthright did something similar with blood powers. 3rd edition whittled most of these types of thing out. 4th edition put the nail in the coffin by taking away random die rolls for ability scores. 4th edition ensures that everything will be fair by ensuring that everything will be nearly the same.
Gamma World’s Getting There
Take a Chance
Characters with random stats, random powers, or other random aspects can provide so much more than mere absurdity. These tools can provide characters that have truly special qualities about them. Whether underpowered or overpowered, when you have to roll to see how a character will turn out, what you end up with is something more unique than is ever possible with the perfectly engineered hero. The pendulum has swung too far towards a very bland brand of balance. I would love to see more games bring back a little chaos and lack of control. When you take a chance and roll the dice you don’t always make something perfect, but you do make something memorable.