Who can name the biggest number?

http://www.scottaaronson.com/writings/bignumbers.html

Try this for size:
Ley A(x,y) be the Ackermann function.
and let B(z) be the busy-beaver function.

J(x,y)=B(A(A(x,y),A(x,y)))

This bad boy is noncomputable and its growth rate will blow your mind.