Have You Played... Shatter?
Smashed it, pet
You'd think you couldn't do much with the brick-breaking genre after Arkanoid and Alleyway, but in 2010 Shatter came along and smashed that theory to bits.
I mean, it didn't redefine what it means to be a Breakout clone by adding a compelling narrative or anything; you must still hit blocks by whacking a ball with your paddle. Still, it does make pretty big changes like sticking your paddle in areas of the screen that aren't the bottom... It's not a morality system, but it's definitely different.
The biggest change to the formula is that you can manipulate the ball's movement beyond just twatting it. Your super-powered paddle is able to push and pull the ball, Jedi-style, so you can actually Roberto Carlos the bastard into a cluster if you're good enough. And you'll need to be good enough if you want to take down the game's block-y bosses. Yeah, it has bosses.
I'm a sucker for a game that fiddles with the tried-and-trusted. Shatter does that and then some.