Article written 06/10/2008 The Prophet of Islam directed believers not to sleep on their stomachs.
Here is the quote from his life time/works-

Ya’eesh ibn Tihfah al-Ghifaari reported that his father said: “I stayed as a guest with the Messenger of Allaah (peace and blessings of Allaah be upon him) with those of the poor whom he hosted. The Messenger of Allaah (peace and blessings of Allaah be upon him) came out in the night to check up on his guests, and saw me lying on my stomach. He prodded me with his foot and said, ‘Do not lie in this manner, for it is a way of lying that Allaah hates.’” According to another report, the Prophet (peace and blessings of Allaah be upon him) prodded him with his foot and woke him up, and said, “Do not lie like this, for this is how the people of Hell lie.”
(Reported by Ahmad, al-Fath al-Rabbaani, 14/244-245; by al-Tirmidhi, no. 2798, Shaakir edn.; and by Abu Dawood, al-Sunan, Kitaab al-Adab, no. 5040, al-Da’aas edn. Also reported in Saheeh al-Jaami’, 2270-2271).

Now of course science didn’t until recently figure out all the issues with sleeping on the stomach. Some of these are-

Due to the weight of the spine, the number one recommendation by doctors to prevent and protect the spine and soft organs is not to sleep this way as the heavy spine sags unhindered as it squashes the internal organs “...You may want to avoid sleeping on your stomach, especially on a saggy mattress, since this can cause back strain and can be uncomfortable for your neck…”….1

More recently too, there was an epidemic so to say of babies dieing in their cots while at sleep, a kind of sleep monster phenomenon. After research and doctors collating data from many mothers to figure out what made infants suddenly die in their sleep it was discovered(after many deaths) that sleeping on the stomach was the single great cause of this SIDS(Suddenqq Infant Death Syndrome)…2

Mothers every where were advised to not put their infants to sleep on their stomachs any more, and prod them with a pillow. The medical profession celebrated their great discovery, great job won’t you say? Even though the religions prescribed the prevention of this years ago.

1… http://www.spineuniverse.com/displayarticle.php/article2023.html
2… http://www.kidshealth.org/parent/general/sleep/sids.html