815. al-Bara' ibn 'Azib reported: 'The Prophet, may Allah bless him and grant him peace, said to me, 'Whenever you go to bed, do wudu' as you do wudu' for the prayer and then lie down on your right side. Then say...'" and he mentioned the rest of it and in it is, "Make that the last of the words that you utter." [Agreed upon] [http://www.answeringchristianity.com/bassam_zawadi/sleeping_of_the_prophet.htm]
Turkish researchers found that people who tend to sleep on their right side have mellower dreams, with themes of relief, joy, peace and love. They also report feeling better rested and less dysfunctional during waking hours. [http://www.huffingtonpost.com/2014/03/07/happier-morning_n_4892107.html]
What about sleeping on your stomach?
This is not allowed in Islam:
818. Ya'ish ibn Tikhfa al-Ghifari said, "My father said, 'Once while I was lying on my stomach in the mosque, a man moved me with his foot and said, "This is a position which Allah hates.
"'" He said, "I looked up and it was the Messenger of Allah, may Allah bless him and grant him peace." [Abu Dawud] [http://www.answeringchristianity.com/bassam_zawadi/sleeping_of_the_prophet.htm]
Erotic and perverse dreams are more common among stomach sleepers than among those who favor other positions, found a Hongkongese study
What about sleeping on the left?
Turkish researchers found that people who usually sleep on their left side have more nightmares and bizarre dreams [http://www.oprah.com/health/Things-That-Influence-Dreams-Dream-Facts#ixzz2vUJ4GvhP]
This is another evidence that Islam is the truth.
The way of the Prophet Muhammad (p) is what we need to practice. Prophets are sent by God. We need to follow Prophetic teachings in order to be successful.
Further reading on this issue:
People having dreams and converting to Islam:
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Jesus taught people to do the Will of God (according to Mark 3:35) in order to become his brothers, mothers or sisters. A Muslim means one who submits to the Will of God. Do you want to become a brother of Jesus? If yes, become a Muslim. Now is the time.
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