Akatsuki no Yona is a must here along with Seirei No Morbito.
Inuyasha is another one.
Kamisama no Inai Nichiyoubi - it has few issues but over all really nice series that deal with adventure and in a way reincarnations/god and etc. MC is not action based but she is likeable. Beautiful animation and soundtracks.
Mai HiME - not adventure based but it is action with magic elements, full of very likeable and memorable female characters who can kick ass.
Romeo x Juliet possibly? Anime differs from classic and has magic and everything.
Senjou no Valkyria: Gallian Chronicles war based but has some magical elements later on.
Soul Eater is another big title.
Toaru Kagaku no Railgun - not adventure or magic but characters have super powers like controling electricity , teleportation and etc.
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