Based on their recreation of the grammar and vocabulary of Proto-Indo-European, some linguists have written short passages in the language, which provide an interesting glimpse into the way our linguistic ancestors were speaking thousands of years ago. These passages are, by necessity, rather simple, given that much of our knowledge of PIE is speculative, and the fact that it was never actually written by its native speakers.

S. K. Sen has translated an extract from Old Indic literature (an IE language) into Proto-Indo-European. Its English meaning is this:

Once there was a king. He was childless. The king wanted a son. He asked his priest, "May a son be born to me!" The priest said to the king, "Pray to the god Varuna."

The king approached the god Varuna to pray now to the god. "Hear me, father Varuna!" The god Varuna came down from heaven. "What do you want?"

"I want a son."

"Let this be so," said the bright god Varuna. The king's lady bore a son.

Following is Sen's translation, written in a simplified form from that used by linguists. There are two points to bear in mind. First, PIE did not use definite or indefinite articles, so "a king" is just "king". Second, the verb usually comes at the end of the clause, so "he asked his priest" is "he his priest asked".
To réecs éhest. So nnputlos éhest. So réecs súhnum éwelt. Só tóso gceutérmm prrcset, "Súhnus moi ccnnhyotaam!" So gceutéer tom réeccmm éweuqet, "Ihkkeswo tteiwóm Wérunom."

So réecs tteiwóm Werunom húpo-sesore nu tteiwóm ihkketo. Cludí moi, phhter Werune!" Tteiwós Wérunos kmmta ttiwós éqqeht. "Qítt welsi?"

"Wélmi súhnum."

"Tótt héstu," wéuqet loukós tteiwos Werunos." Reeccós pótnih súhnum kkekkonhe."

Though is immediately obvious that this language is very different from English and totally incomprehensible to anyone but linguists, there are nonetheless some words and roots which survive, in altered form, in modern Indo-European languages. Réecs, for "king", is obviously the ancestor of the Latin rex, from which derives the French roi and thus the basis of the English "royal". Similarly, phhter is like its English translation, "father", while moi, for "me", is identical in spelling to the modern French, and súhnum is obviously the ancestor of our own word "son".

A slightly longer passage was written in the 19th century by August Schleicher. Instead of adapting a known early Indo-European text to Proto-Indo-European, he wrote a fable of his own, called "The Sheep and the Horses". Our knowledge of PIE has moved on since Schleicher's time, and the passage is now usually written in updated form. One such version is given in Jared Diamond's The Rise and Fall of the Third Chimpanzee; the original update came from W.P. Lehmann and L. Zgusta in 1979, and Diamond himself adapts the text for the benefit of non-linguists, with advice from Jaan Puhvel.

In English the fable reads like this:

On a hill, a sheep that had no wool saw horses, one of them pulling a heavy wagon, one carrying a big load, and one carrying a man quickly.

The sheep said to the horses, "My heart pains me, seeing a man driving horses."

The horses said, "Listen, sheep, our hearts pain us when we see this: a man, the master, makes the wool of the sheep into a warm garment for himself. And the sheep has no wool.

Having heard this, the sheep fled into the plain.

And this is the Proto-Indo-European translation, entitled "Owis Ekwoosque":
Gwrreei, quesyo wlhnaa ne eest, ekwoons espeket, oinom ghe gwrrum woghom weghontm, oinomque megam bhorom, oinomque ghmmenm ooku bherontm.

Odwis nu ekwomos ewewquet, "Keer aghnutoi moi ekwoons agontm nerm widntei."

Ekwoos tu ewewquont, "Kludhi, owei, keer ghe aghnutoi nsmei widntmos: neer, potis, owioom r wlhnaam sebhi gwhermom westrom qurnneuti. Neghi owioom wlhnaa esti."

Tod kekluwoos owis agrom ebhuget.

Once again, the passage looks like Martian (even without the proliferation of diacritical marks found in the first passage) but proves on closer inspection to contain many recognisable roots. Owis, for "sheep", is related to the Latin ovis and the English word "ewe". Wlhnaa is the root of our "wool", keer, for "heart", is an ancestor of the French coeur, and ekwoos, for "horses", is the root of (now extinct) words in many Romance languages as well as horse-related words in English such as "equestrian".
Reference: http://www.cogs.susx.ac.uk/users/geoffs/FAQ_PIE.html. See for an alternate version of the second story.