Here's an alternative to the pyramid shape that everyone else is suggesting:
Just use different types of blocks.
The strongest Lego block is probably one of those thin (1/3-height) 1x1 plates. They are also the heaviest per unit volume. Build the base of the tower using these plates. As you move up the tower, gradually replace them with 1x2 plates, full-height 1x1 blocks, 1x2 blocks, 2x2 blocks, and finally, 2x4 blocks at the top.
Strong, heavy blocks go at the bottom. Weak, light blocks go at the top. This strategy will probably let you increase the height of your tower by at least twice, if not more.
Depends on the increase in crushing weight, if it isn't greater than the increase in weight per lego unit height (~9mm) then you don't get a larger tower in the end.
Just use different types of blocks.
The strongest Lego block is probably one of those thin (1/3-height) 1x1 plates. They are also the heaviest per unit volume. Build the base of the tower using these plates. As you move up the tower, gradually replace them with 1x2 plates, full-height 1x1 blocks, 1x2 blocks, 2x2 blocks, and finally, 2x4 blocks at the top.
Strong, heavy blocks go at the bottom. Weak, light blocks go at the top. This strategy will probably let you increase the height of your tower by at least twice, if not more.