It appears as a new Mode in Melee, alongside Bonus Mode. Coin Mode in Melee only consisted of 3 coins, worth 1, 5, and 10, each. If someone is KO'd, they will lose half of their coins. However, this has been changed in Brawl.
In Super Smash Bros. Brawl and Super Smash Bros. for Wii U
Coin Mode returns in Brawl, with some new mechanics. In Brawl, if a player is KO'd, they will still lose half of their Coins, but they can only lose up to a maximum of 100. Another change is that bills have been added, and are now worth the largest quantity of points. However, they are smaller than coins and float down back and forth very slowly, making them harder to grab.
Coins are produced when any attack hits an opponent. The amount and value of the coins released depends on the strength of the attack. If a player is KO'd, they lose half of their coins, with a maximum of 100 in Brawl, as per stated above. These may be grabbed if close enough to the stage. Often, it is a bad strategy to use projectile moves like that of Bowser's Fire Breath for long periods of time, because the person getting hit with it will rack up points by collecting coins being knocked out of them. On custom stages, one can bounce between spikes and a low platform to rack up coins quickly.