Past and Melee Stages
Past Stages is a special designation given to stages returning from previous installments in the Super Smash Bros. series.
In Super Smash Bros. Melee
In Melee, three Past Stages were available. They are exact replicas of their Super Smash Bros. counterparts, complete with music and backgrounds. All of these stages must be unlocked, unlike in the original game.
From Super Smash Bros.
In Super Smash Bros. Brawl
Past stages in Brawl have been designed a bit differently than their counterparts in the original game. For example, the stages will likely feature enhanced graphics and utilization of the My Music feature. It is unknown if the designation "Past Stages" will continue to be used or if stages from the GameCube installment will be known as "Melee Stages" (as the DOJO!! update was titled). It is also unknown if stages from the original Super Smash Bros. will return. Additionally, it has not yet been confirmed if these stages will need to be unlocked, much like in Super Smash Bros. Melee.
From Super Smash Bros. Melee
Please note that Battlefield is listed as "Special Stage" instead as it has major differences from Melee's Battlefield.