Celtic FC has a large collection of songs.  Here are most of them.

You'll Never Walk Alone

This is a very famous song which has been reproduced by Frank Sinatra, Elvis Presley, Pink Floyd, and Ray Charles.  Liverpool FC also is famous for doing this cheer.  Here is a video of the Celtic supporters before a game versus Barcelona.
http://www.youtube.com/watch?v=A8cffEaZGh0

The Celtic Song
Hail Hail, the Celts are here,
What the hell do we care,
What the hell do we care,
Hail Hail, the Celts are here,
What the hell do we care now...

For it's a grand old team to play for,
For it's a grand old team to see,
And if you know the history,
Its enough to make your heart ,
GO-OH-OH-OH!

We don't care what the animals say,
What the hell do we care,
For we only know,
That there's gonna be a show,
And the Glasgow Celtic will be there.

Sure it's the best darn team in Scotland
and the players they are grand,
We support the Celtic
'cos they are the finest in the land we love them.
We'll be there to give the Bhoys a cheer
When the League flag flies,
And the cheers go up 'cos we know the Scottish Cup
is coming home to rest at Paradise.

There is also a version of this song that Everton sings.

Chorus:

Over and over
We will follow you
Over and over
We will see you through
We are Celtic supporters
Faithful through and through
And Over and Over, we will follow you.

If you go to Germany, you will see us there
France or Spain it's all the same
We'll go anywhere
We'll be there to cheer you
As you travel round
You can take us anywhere, we won't let you down.

Chorus

If you go to Lisbon, we'll go once again
In Zaire you'll find us there
Calling out your name
When you need supporting
You will always know
We'll be right there with you, everywhere you go.

Chorus

Charlie and the Bhoys are a famous Celtic supporter band.  Here they are singing Over and Over and then the Celtic song.
http://www.youtube.com/watch?v=Bl3F9f-jabo&mode=related&search=

Oh Willie Maley was his name,

He brought some great names to the game,

When he was the boss at Celtic Park.

He taught them how to play football,

He made the greatest of them all,

Gallacher and Quinn have left their mark.

And they gave us James McGrory and Paul McStay,

They gave us Johnstone, Tully, Murdoch, Auld and Hay,

And most of the football greats,

Have passed through Parkhead's gates,

All to play football the Glasgow Celtic way.

In '38 there was a show,

And Glasgow was the place to go,

A model of the Tower was football's prize.

England sent four of the best,

They didn't meet with much success,

Because the trophy ended up in Paradise.

And they gave us James McGrory and Paul McStay,

They gave us Johnstone, Tully, Murdoch, Auld and Hay,

And most of the football greats,

Have passed through Parkhead's gates,

All to play football the Glasgow Celtic way.

Well Coronation time was here,

Fifty three, that was the year,

Another four from England met their doom.

They said we'll have to try again,

But like before it was in vain,

Because the Cup is in the Parkhead trophy room.

And they gave us James McGrory and Paul McStay,

They gave us Johnstone, Tully, Murdoch, Auld and Hay,

And most of the football greats,

Have passed through Parkhead's gates,

All to play football the Glasgow Celtic way.

And then in 1957

We faced a guy called Georgie Niven

The game is etched on every Celtic fan,

Wilson, Mochan and McPhail.

And Willie Fernie scored as well,

As Celtic beat the Rangers 7-1.

And they gave us James McGrory and Paul McStay,

They gave us Johnstone, Tully, Murdoch, Auld and Hay,

And most of the football greats,

Have passed through Parkhead's gates,

All to play football the Glasgow Celtic way.

Well ten years, they had gone and so,

To Portugal we had to go,

To play the team that Italy adored.

Celtic went out to attack,

They won the Big Cup and they brought it back,

The first time it had been on British shores.

And they gave us James McGrory and Paul McStay,

They gave us Johnstone, Tully, Murdoch, Auld and Hay,

And most of the football greats,

Have passed through Parkhead's gates,

All to play football the Glasgow Celtic way.

Now it's a new millennium,

We have a brand new stadium,

And we're among the honours once again.

The Celtic fans do proudly say,

Larsson is the king of kings,

And he joins the list of famous Celtic men.

And they gave us James McGrory and Paul McStay,

They gave us Johnstone, Tully, Murdoch, Auld and Hay,

And most of the football greats,

Have passed through Parkhead's gates,

All to play football the Glasgow Celtic way,

All to play football the Glasgow Celtic way.

Willie Maley was a player for Celtic in their first season in 1888.  He was also the manager during the 40s and 50s.
http://www.youtube.com/watch?v=RbmUQMPJ65g

There's Only Two Andy Gorams
This is a humorous chant about the Rangers player Andy Goram who was slightly schitzophrenic.