Breakanoids

also known as: Block kuzushi (Block destuction)

In a Breakanoid the player controls a paddle, which is used to juggle a ball. If the ball falls below the paddle (to the bottom of the screen) then a 'life' is lost. If the ball hits the screen's top, its sides, or obstacles ('bricks'), it will bounce. The goal is to clear the screen of bricks. Variations include a paddle that is tiltable, balls which break through¹⁾ bricks, rather than bouncing off them, the ability to shoot, and so on.

The genre begins, in 1976, with Breakout, which was designed to be a single player response to Pong. In 1986 Taito released Arkanoid, which added a variety of power-ups to the formula. These include: granting the ability to shoot blocks, change the length of the paddle, catch the ball, and so on.
Steve Moraff released Moraff's Blast in 1991, which includes a 'falling wall' mode, and an 'adventure' mode, where the completion of a level is not based upon the destruction of blocks, but striking the exit point.
The 1996 game Blockids added a Z-axis. Though there are 3D Breakanoids released before this, Blockids has the interesting distinction of stacking blocks in three axis; one of those effected by gravity. The player is also able to 'jump' the ball.
Increpare's Paddle Ball²⁾ features a ball that shrinks as the player progresses, as opposed to speeding up. As the ball gets smaller, smaller pieces of the wall are removed. Eventually creating quite striking patterns.
In RDBK, by NEKOGAMES, features a ball whose speed dramatically increased when struck, boucing back to the paddles almost immediately. If missed it is able to bounch of the bottom of the screen, and its speed returns to normal. The game Bricksmash, by Draknek features multiple breakanoids on one board. Each is contained within one of the bricks, and is activated (to play simultaneously with the main game) when struck by a ball.

Breakanoids with a player-controlled character filling the role of the paddle, its wielder, or even the ball itself.

• Firestriker aka Holy Striker (The player walks around a top-down environment, slashing at a moving ball of flame to direct it at blocks, obstacles, enemies and bosses. The goal of each level is to manoeuvre the ball towards the exit, without it leaving the screen.³⁾)
• Gunbarich (Breakanoid in which Gunbird's Marion controls a pair of pinball flippers ⁴⁾)
• Highly Responsive to Prayers (Touhou Reiiden) (in this game—the first of the Touhou series—Reimu interacts with the ball by sliding into it, shooting it, and hitting it with her gohei. Players lose lives by loosing the ball, and being struck by the enemies attacks⁵⁾)
• Kirby's Block Ball (Kirby serves as the ball throughout the game, smashing blocks and enemies alike while guided by moving paddles on top and bottom or all four sides of the screen. At times he wields his own paddle in face-to-face mini-games such as air hockey)
• Thunder & Lightning (NES version - The player controls hungry fellow named Mr. Chin, who is armed with a large stick used to direct a bouncing ball at blocks in its path⁶⁾)
  • Block Carnival (Thunder & Lightning 2)
• Pop'n Smash (each player defends their edge by striking a ball or their opponent with a stick. Each edge has a row of blocks which must be removed before the ball can pass. Anime license. Maybe too Pong-y)
• Zig Zag Cat (the player walks holding a force field in the shape of a paddle, used to bounce a ball (which is actually a cat) at blocks and enemies are along the trail, enjoying power-ups along the way⁷⁾)

Multiplayer competitive breakanoids, though the line gets fuzzy between Breakout or Pong influences

• Ballistix (Played against another human or the CPU, the player attempts to direct a puck through special tiles and through obstacles to end in the opponent's goal ⁸⁾)
• Funny Soccer (2v2 soccer, with each players' paddles being moved as one.)
• Pop'n Smash (Two players swing a variety of sports equipment in order to direct a ball at the opponent's goal, while defending their own⁹⁾)
• Warlords (Four players each guarding a corner of the screen, which is also protected by a mass of bricks/shields)

In place of walls of bricks/blocks, large bosses are found.

• Ghox ¹⁰⁾
• Thunder & Lightning (Arcade version - The player controls hungry fellow named Mr. Chin, who is armed with a large stick used to direct a bouncing ball at enemies in its path¹¹⁾)

• Action Puzzle Prism Land - Lunatic Obscurity article
• Alleyway
• Amegas
• Arkanoid
  • Revenge of Doh
  • Arkanoid DS
• Aquanoid
• Bananoid
• Bat & Ball
• Blocker 3 (versus breakanoid, screen split down the middle.)
• Blockids
• Breakout
  • Super Breakout
• Breakout Invaders
• Breaksout - Play
• Bricksmash - Play
• Brilek
• CASTLEVANIA Xtacy - Play
• Cyberblock Metal Orange
• Geometry (A stage in the pinball game Flipnic)
• Getout: Forever - Play
• EM: Shader Attack
• Goindol
• Gunbarich
• Magical Brickout - Player rotates thr circular playfield, rather than a controller a paddle.
• Moraff's Blast
  • Moraff's Super Blast
  • Moraff's Ultra Blast
• Nervous Brickdown
• No Escape from Ball and Paddle - Play
• Paddle Ball - Play
• Puchi Carat
• RDBK - Play
• Shatter
• Sprint Breakout - Play
• Strikey Sisters
• Super Free Kick - Hardcore Gaming 101 description
• Tecnoball
  • TechnoballZ
  • RadiclBallX
• Wizorb

According to wikipedia:

• Breakout directly influenced Steve Wozniak's design for the Apple II computer — “A lot of features of the Apple II went in because I had designed Breakout for Atari. I had designed it in hardware. I wanted to write it in software now.”[10] This included his design of color graphics circuitry and the now infamous beep and click sound circuitry. It also directly influenced his design of Integer BASIC (which he referred to as “Game Basic”), with his Integer BASIC version of Breakout being the first “proof of concept” application running on the prototype Apple II. His desire to play Breakout on his new computer also led to the addition of a paddle interface, and ultimately the bundling of paddle controllers and a cassette tape containing the code for Breakout for the Apple II's commercial release.
• Pilgrim in the Microworld is an autobiography by David Sudnow detailing his obsession with Breakout. Sudnow describes studying the game's mechanics, visiting the manufacturer in Silicon Valley, and interviewing the programmers.
• For Kid Stuff Records, John Braden recorded a 7-in 33 1/3 RPM record telling the story of Super Breakout. This science fiction story dealt with NASA astronaut Captain John Stewart Chang returning from a routine mission transporting titanium ore from Io to space station New California. He encounters a rainbow barrier, presumably a force of nature, that seems to have no end on either side. He has three lobbing missiles of white light that he can bounce off the hull of his shuttle, and they prove able to break through the layers of the force field. With his life support systems failing, what follows is a test of endurance turned game as he strives to break through the barrier in space.

• Breakout clone - Wikipedia article.
• Breakout variants - Mobygames game group.
• Breaking Down Breakout: System And Level Design For Breakout-style Games - Mark Nelson's genre investigation, at Gamasutra.