A human being is recommended to sleep on his right side, on his left side, and maybe also on the back (though this is less relaxing and shoulder high pillows can tend to form a hunch position so it is useful to be careful), this activity helps in evening pressure on the internal organs and also allows good blood circulation through the body and keeps one side from going sore - especially in the case of stroke patients and other patiends whose bodies can be turned - it is reported in ahadith that the messenger of Allah :saws: recommended making du'aa and starting to sleep from the right side.
وَتَحْسَبُهُمْ أَيْقَاظًا وَهُمْ رُقُودٌ وَنُقَلِّبُهُمْ ذَاتَ الْيَمِينِ وَذَاتَ الشِّمَالِ وَكَلْبُهُم بَاسِطٌ ذِرَاعَيْهِ بِالْوَصِيدِ لَوِ اطَّلَعْتَ عَلَيْهِمْ لَوَلَّيْتَ مِنْهُمْ فِرَارًا وَلَمُلِئْتَ مِنْهُمْ رُعْبًا {18
018:018
:
And you would have thought them awake, while they were asleep. And We turned them on their right and on their left sides, and their dog stretching forth his two forelegs at the entrance [of the Cave or in the space near to the entrance of the Cave (as a guard at the gate)]. Had you looked at them, you would certainly have turned back from them in flight, and would certainly have been filled with awe of them.