I'll try to give you a various list. Sorry it will prob be long and what's sad is that this won't even scratch the surface on the anime music I like, there's just too many haha.
Brothers Conflict opening "Beloved x Survival"
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Code Geass R2 opening 5 "World's End"
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(note: done by FLOW and they do a lot of anime openings that are good. Recommend looking up the band)
Psychic Detective Yakumo opening "Key"
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Blue Exorcist ending 2 "Wired Life" (couldn't find short version)
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K-project opening "Kings"
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Amatsuki opening "Casting Dice"
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Kimi ni Todoke opening "Sawakaze"
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Toradora! opening "Pre-Parade"
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No. 6 opening "Spell"
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Zoku Natsume Yuujinchou ending "Aishiteru"
(My absolute favorite from my favorite anime, the melody and words are so peaceful to me.)