There are various attacks in the Smash Bros. series that cause the flame effect. Targets hit by these attacks will momentarily be set on fire, flashing red and orange. Flame attacks have other effects:

Flame is by far the most common "elemental" attack in the Smash Bros. series, with over half of Brawl's roster having access to at least one.

The vast majority of explosive attacks use the flame effect.

List of flame attacks by characters

List of flame attacks by items

List of flame attacks by enemies and bosses

Meta Ridley's Fireballs (all kinds)