Why is the number seven special? God seems to favor the number seven and I'm not sure why. Is there a reason, or is this just His favorite number? 

You'll notice that God not only uses the number seven, but multiplies other numbers by seven as well. Please provide scripture and let me know if there are other numbers that God uses.
I think this answer from the Judaism site sums it up:


  7 is the length of time for a natural cycle to transpire, often ending
  with holiness/sanctification of some sort (the pattern set by
  creation)


7 is special because it was set down by God as the natural cycle in creation.



In the same question above is this answer about other numbers:

It mentions the numbers:


  1, (2?), 4, (5?), (6?), 7, 8, 10, 12, 40, and 70 all have
  significance.


See that answer for full details of their importance.



Also important is the number 50 for Jubilee (from this answer):


  Toward the end of the book of Leviticus the 7 day measure that is most
  familiarly the Sabbath is unrolled across years to be the sabbatical
  year, and across decades to be the Jubilee. The Jubilee is the 50th
  year - the crown of the 7th 7.