 If you liked
Higurashi no Naku Koro ni Kai
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 ...then you might like
Suzumiya Haruhi no Yuuutsu (2009)
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Although Higurashi is less repetitive, both are second seasons with the idea of an 'eternal summer', only one person who remembers all of it, deja vu with the other characters, and a 'god' behind all of it.
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Recommended by konataismyhero
The similarity shared with Endless Eight becomes apparent late at season 1 - with Rika being the keeper of time, and resets time in order to reach a happy ending, similar to the role for Yuki. Other characters eventually pass over memory between other loops and help to change fate. Even though being a Haruhi fan, I must say that Higurashi executes this much better in comparison.
Both series feature mysterious elements such as aliens and infinite time loops/infinite summer/Endless Eight.
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Recommended by OtameganeJoe
Both series have the cast stuck in a time loop during the summer with only one person knowing through every loop and trying to change the outcome of that loop.
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Recommended by Gray_apothecary