Building the Base
Build a wide, sturdy base. When building large towers, leaving large, open spaces in the structure saves goo balls. As the tower gets higher, you can take parts out of the extra bulk of the base to add to the height of the tower.
Reinforcing the Tower
While building the tower, some parts of the resulting structure may become too weak and narrow. Before making the tower too much taller, you can put extra weight on the top, intentionally causing it to bend at the narrow point; when points of the tower come close enough, you can connect more points in the tower, and then take the extra weight back off of the top. When the tower straightens back up, the narrow and weak section remains reinforced.
Work Quickly
Some levels have time limits, but in general you will want to work quickly. Over time, towers sway more and destabilize as the goo shifts.
Timebugs
Timebugs can give you the opportunity to rewind and correct some mistakes. If you make a mistake that causes a tower to fall, timebugs can restore some precious time to correct that mistake.