Teeter
Teetering is an animation that is naturally activated by standing near a ledge in all four installments of Super Smash Bros. The character will automatically start teetering back and forth over the edge with a panicky expression.
The effect can only be done when a player walks towards the edge slowly. Simply landing near the edge does not count, and moving too quickly will simply cause the character to run off the edge. While teetering, a character will not walk off the edge unless the control stick is tilted past a certain amount; otherwise, the animation is an easter egg and does nothing but alter the character's standing animation. That said, it is possbile for a teetering character to dodge an attack that would have hit them were they standing up.
Characters will teeter regardless of whether the edge they are hanging over can be grabbed onto. Characters will stop teetering if they take any action (such as attacking).
Gallery
Link teetering in Hyrule Castle, in Super Smash Bros..
Marth teetering in Yoshi's Story, in Super Smash Bros. Melee.
Lucario teetering in Spear Pillar, in Super Smash Bros. Brawl.