Background character

Background characters are, as the name implies, characters that appear in the background of some stages, they will appear in a stage that correspond to their home universe (e.g. King Dedede appears in the Super Smash Bros. stage Dream Land). Note that background characters shouldn't be confused with stage hazards.

In Super Smash Bros.

Congo Jungle

• Necky appears flying in the background.

Dream Land

• King Dedede and Bronto Burt appear flying in the background.
  

  King Dedede as a background character in Dream Land

Mushroom Kingdom

• Many classic enemies from Super Mario Bros. are seen in the background.

Planet Zebes

• Several enemy sprites ripped directly from Super Metroid, including Ridley, can be seen flying around.

Saffron City

• Several flying-type Pokémon, including but not limited to Pidgey, Fearow, Moltres (rare), and Butterfree, fly across the skyline.

Yoshi's Island (SSB)

• Shy Guys appear in the background.
• A Goonie, in its Yoshi's Story design, occasionally flies in the background.

In Super Smash Bros. Melee

Brinstar

• A Chozo Statue on the main platform comes to life and briefly walks before settling down into its original position.
• There is a large organism in the far background that shakes constantly, and is heavily speculated to be Mother Brain, though this organism lacks the characteristic features of Mother Brain herself, such as the one eye and spikes.

Brinstar Depths

• Kraid emerges from the lava and swipes at the stage, turning it clockwise or counter-clockwise.

Fourside

• Porky Minch appears in his helicopter.

Great Bay

• After three minutes have passed, the Four Giants appear on the hillside to push the falling moon back into the sky (This is in reference to the fact that Link had three days to wake said giants and prevent the Moon from falling).

Jungle Japes

• Cranky Kong is seen walking back and forth in his cottage and rocking in his chair at various times (also seen in Brawl).

Yoshi's Island (SSBM)

• A Fishing Lakitu and a Banzai Bill fly around in the background.

Yoshi's Story

• Pak E. Derm can be seen walking behind the scenery.

In Super Smash Bros. Brawl

Regardless of stage and game mode, using Pokémon Trainer will have the Trainer himself stand on a platform in the background. As with the previous games, there are stage-specific background characters as well.

75m

• The original Donkey Kong appears on the top of the stage, as in the original game.

Distant Planet

• A Red Bulborb sometimes appears to the right as part of the stage, and also in the background.

Frigate Orpheon

• The Parasite Queen, the first boss of Metroid Prime, appears in the background in Frigate Orpheon.

Green Hill Zone

• Tails, Knuckles, and Silver can be seen running up and down the shuttle loop.
  File:Greenhillzone3.jpg

  Tails, Silver, and Knuckles.

Luigi's Mansion

• Boos briefly appear from the rubble of the mansion when it collapses.

Pokémon Stadium 2

• Electivire, Magnezone, Snorunt, Snover, Drifloon, Hoppip, Skarmory, Cubone and Dugtrio all appear in the background of the various elemental transformations of the stage.

Shadow Moses Island

• Occasionally, Metal Gear REX, Metal Gear RAY, and two GEKKO will appear in the background of the stage.

Smashville

• Villagers from Animal Crossing appear in the background, depending on actual time of day and date, including Villager, K.K. Slider, Tom Nook, and others.

Spear Pillar

• Dialga, Palkia, and Cresselia appear on occasion in the background of the stage. Their attacks can affect gameplay or alter the terrain of the stage.
• Uxie, Azelf, and Mesprit may occasionally appear on the stage at random.

Yoshi's Island (SSBB)

• For a third time, Shy Guys appear in the background, with Support Ghosts, Chain Chomps and Goonies also occasionally appearing.