It's been mentioned but seemingly not linked, but I really did like Spice and Wolf S1's intro. It just seemed so eminently suitable.
Here's a mix I made earlier:
(Original, with additional guitar track, I did the mix but didn't play the instrumental so I can't take much credit)
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Also haven't seen it mentioned but I like a lot of Angel Beat's music, not limited to the Op/Ed but here:
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Also, the fact that multiple tracks were available in both guitar and piano/classic variants obviously suited more than just my tastes:
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Also as an extra:
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K-On!!'s "No, Thank you!" also gets a mention, one of my favourite tracks from the show, even if I prefered the first series to the second.