I hum to my cat, going back to the time she was a kitten. She would be lying next to me, or on me, and get her little purr motor running as a sign of her contentment, and I would hum back as a sign of mine.
It actually seems to have worked. Now, twelve years later, if she’s sitting or lying near me and I start humming, odds are good that she will stretch out and close her ees.
It’s also a great time of year for kitty carols.
my very shortened dreidel kitty song is “kitty kitty kitty I made you out of purr”
(Sorry, I’m not Jewish so that’s all of it I know.)
Of course, there are also “jingle cats jingle cats purring all the way”
Someone on the SDMB originated the rewritten ‘Little Drummer Boy’ about their cat’s butthole display. I only remember, “it’s pink! it’s pink! and it doesn’t stink/cuz I wash it with my tongue/cuz i wash it with my toooonnnge.”
Oh, You are my Cat, You’re the Great Sable Cat!
I don’t care that you are Shy… You’re my Kitty kind of Guy
in the morning with glee, my lap you do see (and hop in!)
Morning, King of my Mews!
to King Herod’s Song from Jesus Christ, Superstar*
*actually, I am an unrepentant Pagan.
I sing-song chant this at Brown Cat:
*I am a little kitty and I don’t want to be a pig,
Because kitties are so pretty and pigs roll in the mud.
I am a little kitty and I don’t want to be a fish,
Because kitties are so pretty and fish live in a bowl.
I am a little kitty and I don’t want to be a dog,
Because kitties are so pretty and dogs have no brain.*
Repeat as long as I can think of other animals/politicians/inanimate objects that the kitty does not want to be.
Since I sing often around the house, I have discovered that many, many songs can be all about the kitties if you insert “kitty, kitty” into them at intervals–at least, the kitties think so. They don’t understand the rest of the lyrics anyway.
It’s familiar, and works with any two-syllable pet name. Two syllables seems about right for a name for a pet.
Awwww! Tikva is such a pretty kitty!
My dog Ruby gets to hear “Ruby dooby doo, be dooby dooby…” to the tune of Sinatra’s Strangers in the Night (not Scooby!). She also gets the Beach Boys “Don’t Worry Baby” chorus in the car, cause she gets nervous.
My cat Roland Kerzweil gets to hear “Rollin, rollin’, rollin…” from the old tv show Rawhide.
They all get to hear “It’s a Beautiful Morning” when it is.
They also hear Kitty on My Footby the Presidents of the United States of America alot.
Dont sing to her, but I talk with her. i will also channel her in conversations to Rob =)
Every morning and every evening he like to pick her up and do the bouncing baby dance with her, and I insert her conversation, stuff like ‘where are my treats, butthead’ and “stop bouncing me before I yack hairballs all over you butthead”
It is really funny, because she will wave all 4 paws in the air, and purr loudly, she really likes the attention. She gets a hairball treat and an osteo joint treat every morning and evening, she is all about the treats =)
Sung to the tune of “Goldfinder”"
Bob RANGER! He’s the dog with the Miiidas touch!
Sung to the tune of “Both Sides Now”
Cleo Cleo Cleo Rose
She’s got gray fur, she’s got six toes
And why I love her know one knows
I love her anyway.
Sung to the tune of “Brahms Lullaby”
Mickey Cat, Mickey Girl
Mickey Mona, I love you.
You’re a good girl, not a bad girl
Mickey Mona I love you.
Sung to the tune of “Stairway to Heaven”
There’s a kitty who bites
her mommy at night
And her name is Mi-icky Mona.
I also sign “Lady” by Styx to Skunk Marilyn and Cleo Rose, only it’s “Ladies”. Mickey Mona is dead so I don’t sing it to her.
Oh lord, I’d forgotten that one… We have a Doberman with a cropped tail, and with the little bare spot at the end, it kind of looks like a monkey’s finger. Thus:
Monkey Finger!
Lil’s the dog, the dog with the monkey’s touch…
It’s on her buuuuuuutt!
My only hope of lasting fame. 
Let me help you out there.
*I had a little kitty
I made her out of purr
And when she’s cute and poofy
It’s time to stroke her fur.
Oh, kitty kitty kitty
I made you out of purr…*
She is not my dog… She belongs to the wife and kids. But she is sort of cute and fluffy. So, I often sing songs and insert “fluffy” into the lyrics somewhere. Sometimes I do a cover song, and sometimes I make it up. I don’t recall any certain lyrics, but one time I had what I felt was the perfect song. I never did write it down, so I’ve lost it. Now, when I sing something, my daughter asks if it was “The” fluffy song…
Thanks for making me realize I’m not alone in this world.
Pluggy is a puppy dog.
She’s black and white, and smelly.
When she’s good, I give her treats
And rub her on the belly.
When she’s bad, I get mad
And lock her in the closet.
Just to show me who’s the boss
She leaves a small deposit.
Music for those inclined to sing along.
stupid dog’s been dead ten years and I still sing it to her…
Miso Miso pretty little girl
Miso Miso prettiest cat in the world
I love my Miso.
My daughter says the tune reminds her of Fish Heads so now I’ve taken to singing:
Miso Miso rolly polly Miso
Miso Miso Eat her up YUM!
But it makes her nervous when I sing it like that.
Oddly I don’t have a song for Wonton. I think it’s because he is always on me. Miso has to be coaxed out of hiding places.
(clears throat) To the tune of Born Free: “Maaarco! My kitty’s named Maaarco! And kitty named Marco is one big furry fluff baaaaalll! Maarco, you eat all the kibbles, you don’t just take nibbles, you stuff yourself to the maaaaxxx! MAAARCO…” etc.
I sing along to music sometimes, though I have a voice that would drive away serpents, and Marco doesn’t mind as long as I don’t sing too loud. Today I sang counterpoint to “Mull of Kintyre” and he purred right along, undismayed.
I am completely tickled by all of the responses so far! 
Plus it’s a simple, clear declaration of affection. And for me, every single part of it is so freaking true:
You are my sunshine, my only sunshine = I’m currently single, and she is the brightest spot in my life
You make me happy when skies are gray = She always cheers me up/puts a smile on my face
You’ll never know, [dog], how much I love you = Can’t get much truer than that
Please don’t take my [Bailey/doggy/puppy] away = Of course I don’t want anything to ever happen to her
I wouldn’t consider this a “song,” but I sort of sing to them when preparing their food. I like to tell them what flavor they’re getting.
“Oh boy,
Two hungry kitties are getting Turkey & Cheese.
Two good kitties,
Two good pussycats,
One black kitty and a tabby with a fluffy tail,
Getting Turkey and Cheese.
Oh boy.”
By now, they’re both adding their own vocalizations to the mix.
Now you guys have inspired me to get a little more creative with this.
Man, you guys are creative! The best I can do is sing Spanish pop songs with my kitty’s name inserted.
Estoy tan enamorada
De mi gato Santito
Que cuando se va de casa
Triste me pongo
(I’m so in love
With my cat Santito
That when he leaves home
I become sad)
Sounds better in Spanish!
You’re a budgie bo-oy,
with your budgie to-oys
They’re plastic
You’re fantastic!
To Barbie Girl, if it wasn’t inanely obvious.
I also quote mock Shakespeare at him every night as I go to bed;
Goodnight sweet budgie, may flights of birdies sing thee to thy rest
But mainly he says “Chirp chirp!” and I say “Good boy!” then he says “Chirp chirp!” and I say “Good boy!” over and over again until the kid pleads with us to stop.