What a great thread!
Faeriegirl, I love that Frente song! That's a great one to sing to baby.
I sing 'This Old Love' by Lior:

We'll grow old together
We'll grow old together
And this love will never
This old love will never die

Also, she gets the hiccups all the time and they inevitably pi$$ her off, so I try to sing to her to distract her. I made up one - 'Oh Hiccupy Baby', but last time I made myself laugh by singing 'My Little Hiccup' to the tune of 'My Little Buttercup' - very sad I know!