From SmashWiki, the Super Smash Bros. wiki
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"Normal" may also refer to one of the five difficulty levels.
Marth getting hit by Mario's up tilt in SSB4, a normal attack

Normal, officially known as battering, is an attack effect in the Super Smash Bros. series that debuted in Super Smash Bros.. It is the default attack effect, so does not have any special properties.

Normal attacks are resisted by Battering Resistance stickers in Super Smash Bros. Brawl's The Subspace Emissary.

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