Why do Jews rock while they pray?

There are several reasons – here are some. 1. The verse (psalms 35; 10) says "all my bones will speak" referring to the praise of Hashem and that can be done through moving the whole body during the Tfilah. (Rema OC 48; 1) 2. The verse (Malachi 2; 5) says "before my name he will bow" which is again a reference to the rocking during the Tefilah (Magen Avraham ibid, he also adds that there is a kabalistic reason too.) 3. The verse (Shmot 20; 14) states that the people trembled before Hashem, that too can be a reference to the Tefilah. (Tur ibid) 4. It's a habit the evolved from the fact that several students shared the same book and every time someone else bent down to see the writing. (Kuzari 2, 80)