My favorite song that was sung on I Love Lucy was We're having a baby, my baby and me.

By the Light of the Silvery Moon,
(Stompin' at the Savoy is kinda nice, too).

We are Friends of the Friendless!

j/k -- there are many, MANY wonderful songs on this show... I still like "Babaloo", the signature song.

Sweet Sue and Glow Little Glow Worm top my list!

I was at Barnes And Nobles during my birthday,
ok actually a bit AFTER my birthday,and just
looking around I found a CD in the music department titled DESI ARNAZ' GREATEST HITS.

It included of course Babaloo,which was his
signature song.

Note:I wonder how many people realize that
Desi Arnaz was a band leader in real life as
well as playing one on tv?
After it is his band that plays the title theme
to I Love Lucy.

There is a terrific music short, circa 1946 of Desi Arnaz and his band in a nightclub setting. There's great camerawork and a female singer (unidentified) who looks like Lucille Ball! Arnaz wasn't much of a singer, but he had great presence
and was a quite good conga drum player. This short
can be found on a video called Swing, Swing, Swing. I can't recall which volume.