Re: what direction do plant roots grow in and why do they grow this way?

Yes, the phenomenon you describe is known as positive gravitropism.  That is, 
the roots of a plant grow in the same direction as the gravity vector.  The 
shoots of plants, on the other hand, exhibit negative gravitropism, or growth in 
a direction opposite that of the gravity vector.  The mechanism by which 
this occurs is not entirely clear, but near the tips of the plant roots there 
are specialized gravity-sensing cells which contain heavy, starch-filled 
organelles called amyloplasts (there are similar organelles in the mammalian ear 
which help us keep our balance!).  It is thought that when these cells are 
displaced with respect to the gravity vector, the amyloplasts settle to the 
lower side of the cell, and this is how the root senses its orientation.  If you 
reorient your root seedlings, you should find that the roots will reorient 
themselves to grow downwards.  Many fungi also exhibit negative gravitropism, 
but the mechanisms by which they do so are less clear.  
Check out 
Space Biology of Plants for more information.