As a mystery I can't think of any atm however there are passive double atks by Kurotsuchi, Jinchuriki Fu (I think), Onoki (I think).
Those that atk x2 themselves are like Suigestsu and Zabuza.
Can't think of more atm

Rock Lee (only through his mystery)

Eight Gates Lee

Suigetsu

Mist's 7 Ninja Swordsman Zabuza

Sakon and Ukon

Mifune

Darui (only while his barrier is active)

Samehada Killer Bee (only through his mystery)

Killer Bee (only through his mystery)

Great Ninja War Hinata (only through her mystery)

Kubikiribocho Kakashi

I think that's about all I can remember

Light Main has 2x attack if you use Bloodthirsty Demon.

Fu buffs double attack in the first round (meaning all your ninjas use standard attacks twice in the first round only), although she doesn't do double attack.

Chojuro attacks twice.

Kabuto heals two ninjas per standard attack.

Only ones I know that haven't been named are Akatsuchi and Onoki.

Chojuro ;)

And Lightning main can give itself up to like, 4-5 standards (More if they kill)

Another thing to note here is that 8Gates Lee and Ukon/Sakon are the only characters whose extra attack can be activated twice per turn. If paired with someone who provides extra Standards, they both can pull off four attacks per turn.

Kurotsuchi is another one that gives extra standard attack.