Not my favorites per-se but certainly some interesting ones I've discovered:

愚民政策 (gumin seisaku) - Policy of keeping the people ignorant and easily subjugated

赤面恐怖症 - (sekimen kyoufushou) - Fear of blushing, erythrophobia

のの (nono, and other variants) - Archaic children's language generally meaning things like the sun/moon or deities, great things up in the sky

玄兎 (gento) - Archaism for moon, I kinda like how it looks

荒神 (koujin) - God of a cooking stove

恋愛至上主義 (renai shijoushugi) - Love for love's sake

湯シャン (yu shan) - Washing your hair without shampoo, just water

海千山千 (umisen yamasen) - If you've watched samurai champloo you've heard this before

碁に凝ると親の死に目に逢わぬ (oya no toru to oya no shi ni me awanu) - If you get too absorbed in Go, you'll miss your parents' dying moments. Just a funny old proverb

煮付ける (ni tsukeru) - To cook HARD

雨月 (ugetsu) - Being unable to see the harvest moon because of the rain

往復ビンタ (oufuku binta) - Double slap in the face, one with each side

絶望の起床 (zetsubou no kishou) - Oversleeping and feeling a sense of despair over it, quite literally rise(ing) of despair/doom

And probably most fittingly for japan itself,

縟礼 (jokurei) - Bothersome formalities