How many LEGO bricks exist in total?
It does not seem as if it would ever be possible to come to a definitive assertion—or even a sufficiently precise  approximation—of "how many LEGO bricks exists." For the English Wikipedia article "Lego" in the "Manufacturing" section informs,


  Annual production of Lego bricks averages approximately 36 billion, or about 1140 elements per second.


Although this quotation conflates "bricks" and "elements" thereby ambiguating whether it refers specifically to bricks or generally to any LEGO component, it nevertheless indicates that the number of LEGO bricks is indefatigably increasing. Thus, even if a total number of LEGO bricks in existence could be concluded, that number would immediately be inaccurate as a result of additional bricks continuously manufactured. Furthermore, as Eran perceived in the comments, LEGO bricks eventually disintegrate or become unidentifiable as LEGO; therefore, even if there were documentation of exactly how many bricks were produced up to any given time, it would still be infeasible to establish how many LEGO bricks exist because it would be extraordinary difficult to ascertain which individual LEGO bricks are currently in existence.