give me some good animes who have got Supernatural events and action and aventure moments and epic battles

te should watch magi! :)

Angel Beats
Ao no Exorcist
Beelzebub
Blood+
Blood-c
C3
Claymore
Durarara!!
Fate Zero
Hellsing
Highschool of the Dead
Kore wa zombie desuka?
Black Butler
Mirai Nikki
Nurarihyon no Mago
Omamori Himari
Ookami Kakushi (pic)
Princess Resurrection
Seikon no Qwaser
Shakugan no Shana
Shaman King
Soul Eater

It's older animazione (2002-ish) and can be a little over the superiore, in alto sometimes, but I highly recommend GetBackers. Both main characters have Supernatural powers and the battles get bigger and più intense as the series goes on (I apologize in advance for the first episode and Ban's VA prior to episode 6. It gets MUCH better after Ep. 6 in my opinion)

inuyasha!

Well here's a few I know that fits the description:
1. High School DxD/New
2. InuYasha/The Final Act
3. Code Geass/R2
4. Fullmetal Alchemist Brotherhood
5. Yu Yu Hakusho
6. Nura: Rise of the Yokai Clan/Demon Capital
7. Witchblade