Question

What are the new legendaries in Sun and Moon?

Answer 1

Mascot Legends: Solgaleo, Lunala.
Tapu Legends: Tapu Koko, Tapu Fini, Tapu Bulu, Tapu Lele.
Ultra Beasts: Nihilego, Buzzwole, Phermosa, Xurikitree, Kartana, Celesteela, Guzzlord.
Other: Necrozma, Magearna.

There's also Marshadow, but I'm pretty sure that it's more of a mythical Pokemon than a legendary, plus you can't even find it in-game.
Note: I'm not 100% sure if the UB's are counted as "Legendary Pokemon" but I'm putting them on this list because they seem to be similar to most legendaries.

Source

Comments

The Ultra Beasts Nihilego, Buzzwole, Phermosa, Xurikitree, Kartana, Celesteela and Guzzlord may count as well.

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The UB's count as well

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Magearna? :/

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UBs and Tapu's aren't officially Legendary Pokémon, but they're rare and can't breed so they're pretty close.

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I believe Magearna is a Mythical Pokemon actually.

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Ahem. Mythical Pokemon are a class of Legendary Pokemon.