From SmashWiki, the Super Smash Bros. wiki
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Marth getting hit by Mario's up tilt, one of many normal attacks.
"Normal" may also refer to one of the five difficulty levels.

The normal effect (known as Battering by the stickers of Super Smash Bros. Brawl) is the term used to describe the "regular attack" effect; that is, an attack that is not accompanied by any elemental properties (e.g. flame) or other special effect (e.g. slash). By definition, the normal effect has no special characteristics. However, there are many visual and auditory differences among normal attacks; an example being the first 2 hits of Mario's neutral attack being punches and the final one being a kick. There are no stickers that power up the effect, but there are some that grant resistance to it.

As the normal effect is the default (and thus overwhelming majority) effect of all hitboxes, maintaining a list would be futile, and any attacks that are not listed on any other effect pages can be assumed to be normal.