Good Birkat HaChodesh Tunes (from a not-so-religious Jew)

Cheshvan – This is Halloween – Nightmare Before Christmas (10/31 usually falls within Cheshvan)
Kislev – Maoz Tzur (pretty obvious as to why it’d be chosen)

Tevet – same as Kislev (Rosh Chodesh Tevet ALWAYS falls during Hanukkah)

Shvat – HaShekediat Porachat (most widely-known Tu BiShvat song)

Adar (doesn’t matter how many there are) – any well known Purim song (no explanation needed)

Nissan – Simcha Rabah or Mah Nishtanah (no explanation needed)

Iyar – Kachol v’Lavan (I sung this song at Yom Haatzmaut celebrations when I was in grade school/middle school)

Sivan – the niggun used to memorize the books of the Tanakh (I don’t know the actual name) (the niggun starts by naming the books of the Torah)

Tammuz – Yerushalayim Shel Zahav – Naomi Shemer (Tzom Tammuz involves the breeching of Jerusalem’s walls)

Av – Imagine – John Lennon (about imagining a world w/o hatred – the opposite of what happened of Tisha B’Av)

Elul – Happy New Year – ABBA/A*Teens (the new Jewish year is fast approaching)

(What are your ideas for Birkat HaChodesh tunes – preferably from pop culture?)