I`ll try to list just one from each musical.

All That Jazz- Chicago
The Wizard and I- Wicked
As If We Never Said Goodbye- Sunset Boulevard
Music of the Night- Phantom of the Opera
The Dark I Know Well- Spring Awakening
Everyone`s A Little Bit Racist- Avenue Q
Another Day- RENT
Take Me Or Leave Me- RENT I couldn`t just pick one song from Rent
Shy- Once Upon A Mattress
The Worst Thing I Could Do- Grease