A slightly longer version of this poem is common (with a number of variations):

I have a spelling chequer,
It came with my pea sea,
It plainly marques four my revue
Miss steaks eye cannot sea.
When eye strike a quay, right a word,
I weight four it two say
Weather eye am wrong oar wright
It shows me strait aweigh.
As soon as a mist ache is maid
I nose bee fore two late
And eye can put the error rite
Its rarely, rarely grate.
I've run this poem threw it
I'm shore your pleased two no,
Its letter perfect in it's weigh
My chequer tolled me sew.
--Unknown

And this one is even longer (and better IMHO):

An Owed to the Spelling Checker

I have a spelling checker
It came with my PC
It plane lee marks four my revue
Miss steaks aye can knot sea.
Eye ran this poem threw it,
Your sure reel glad two no.
Its vary polished in it's weigh
My checker tolled me sew.
A checker is a bless sing,
It freeze yew lodes of thyme.
It helps me right awl stiles two reed,
And aides me when aye rime.
Each frays come posed up on my screen
Eye trussed too bee a joule
The cecker pour o'er every word
To cheque sum spelling rule.
Be fore a veiling checkers
Hour spelling mite decline,
And if were lacks or have a laps,
We wood be maid to wine.
Butt now bee cause my spelling
Is checked with such grate flare,
Their are know faults with in my cite,
Of non eye am a wear.
Now spelling does knot phase me,
It does knot bring a tier.
My pay purrs awl due glad den
With wrapped words fare as hear.
To rite with care is quite a feet
Of witch won should be proud.
And wee mussed dew the best wee can,
Sew flaws are knot aloud.
Sow ewe can sea why aye dew prays
Such soft ware four pea seas.
And why I brake in two averse
By righting want too pleas.

--Jerry Zar, Dean of the Graduate School
Northwestern Illinois University