Anyway, thought it would be good if I could start collecting some of these.

Here’s the first one:

Wherever we go, (Wherever we go),

People want to know, (People want to know),

Who we are, (Who we are),

So we tell them, (So we tell them),

We are house name, (We are house name),

Mighty, Might house name, (Mighty, mighty house name)

Repeat two more times, getting steadily louder.

Another one:

Two, four, six, eight

Who do we appreciate?

House Name!!!!!

Or a variant of that:

One, two, three, four,

Who do you think we’re barracking for?

Five, six, seven, eight,

Who do we appreciate?

(shout) House Name!!!!!

This one from Sydney Grammar might be able to be modified:

Alligator mince meat

Crocodile pie

V-I-C-T-O-R-Y

Are we in it?

We say YES

We are the boys from S-G-S

G-R-A-M-M-A-R, Grammar!!!!!

You would need to change SGS and Grammar at the end, making sure the SGS syllables fit in.

Or you could be a little bit naughty:

Rah rah ree
Kick ‘em in the knee
Rah Rah rass
Kick ‘em in the other knee

Or this:

What do we eat?
What do we eat?
Wolf meat!
Wolf meat!
How do we like it?
How do we like it?
RAW! RAW! RAW!

This one’s funny:

Gimme a B! (B!)
Gimme an L! (L!)
Gimme a B! (B!)
Gimme an L! (L!)
Gimme a B! (B!)
Gimme an L! (L!)
(repeat as desired)
What’s that spell? BLBLBLBLBLBL!!! (in which everyone does that thing where you wiggle your finger between your lips and make that underwater fishy sound)

Another silly one:

Peel! Bananas! Peel peel bananas! (Accompany with banana-peeling motions)
Throw! Bananas! Throw throw bananas! (Accompany with banana-throwing motions)
Stomp! Bananas! Stomp stomp bananas! (Stomp rhythmically on floor)
Go! Bananas! Go go bananas! (Wave hands up in air, do silly things, hop around in a circle, etc.)

Or:

[Team name] is what? Dynamite!
[Team name] is what? Dynamite!
[Team name] is tick-tick-tick-tick-tick-tick-tick-tick-BOOM Dynamite!
(Accompany the tick-tick part with hands going from at sides to above head like the hands of a clock, meeting above head in a clap at Boom.)

This one could be good, and a little naughty if your team is called Cobras:

Cobras! Cobras!
Comin’ through the grass!
You better watch out
Or we’ll bite you in the knee!

Another little rhyme:

Pork chops, pork chops
Greasy, greasy
We can beat (other team)
Easy, easy!

I remember this one from my school days:

Roll out the carpets

Roll out the mats,

Come on (House Name),

Knock ‘em flat!!

If you know of any others, especially ones that can easily be changed to suit, leave them in the comments.