Why do some people have the custom to wind the Tefillin-Shel-Yad towards themselves, while others wind it away from themselves? What is the reason behind these two customs, and which sects of Judaism generally follow which method?
It's pretty much a question of which eida you come from:
Ashkenazim wind inwards, Sfaradim wind outwards.
The link that @jake posted in comments illustrates this very nicely - it depends on which eida's minhag you use.
(Sorry, I don't know the reasoning behind the different minhagim - though I find it likely that each do it that way, because thats the way they do it...)
In my (predominantly Ashkenazi) school where we learned about Tefillin, we were taught that the reason for wrapping inwards is that it is towards your heart, thereby making a statement (over the top...) of the love that you (... towards your heart) has for the mitzvah of Tefillin.