I used to date a girl who wrote words to the SMB theme, and to this day I still sing what I can remember;

Nin-ten-do, It's Mario
He is the plumber with bright red overalls
He is fighting to save the Princess Peach,
From Koopas and Goom-bas-too

that's all I remember. But my wife, in jealousy of this, wrote lyrics for World 1-2.

Oh my gosh it's scary
Oh my gosh it's scary

That's it, but it really works. Trust me.

(plus, it sounds like "Oh my gosh it's Gary," which makes no sense and makes it that much more fun.)

I got the album with that song at home. Mario and Zelda Big Band Live CD. It is actually wicked.

Agreed, that CD is pretty awesome. The Wind Waker songs are really nice.
... *loads it up on iTunes*

Of course it has words. This is how it goes:

Swing your arms
from side to side
Let's do the Mario!
All together now
Swing your arms
from side to side
Let's do the Mario!
All together now
Just---like---that