Why does the Tower of Hanoi problem take $2^n - 1$ transfers to solve? According to http://en.wikipedia.org/wiki/Tower_of_Hanoi, the Tower of Hanoi requires $2^n-1$ transfers, where $n$ is the number of disks in the original tower, to solve based on recurrence relations.
Why is that? Intuitively, I almost feel that it takes a linear number of transfers since we must transfer all but the bottommost disc to the buffer before transferring the bottommost disc to the target tower.

Your intuition is right.  All but the bottom disk must be moved TWICE, so you should expect (one more than) twice the number of transfers for one fewer disk.  We have $$2(2^n-1)+1=2^{n+1}-1$$
