World of Goo is an incredibly unique game that does some very interesting things with building. It's also a rather difficult game at times. There are a few tips that should really make the whole game a lot easier if you keep them in mind though.
This is a Physics Game
This should be obvious, but it can be easy to forget that the central theme of this game is physics. You are trying to get these little Gooballs to make the buildings you need. They are limited by the games physics though. If your tower is swaying badly, then you need to fix that before you go any further. Remember to keep the weight fairly balanced on both sides. Once it starts swaying, it is really hard to stop it without using a time bug.
You should also learn to balance your goals well. Most levels challenge you to make a strong structure with the least Goo possible. This is challenging, since the most effective way to do this is usually to make a narrow tower. Narrow towers are the least stable though. Figure out a good blend between the two strategies. A good setup is usually to have about 5 or 6 Gooballs forming a strong square base.
Anchors Away
If you are building a big tower or bridge, remember to use anchor points. These are just simple extensions from your main structure that rest on something firm. My personal favorite is to have a Gooball on each side of my tower's base. Then it forms a triangle that presses against the ground if it starts to sway.
Timebugs are Your Friends
Don't forget about the timebugs. These little white insects are your best friend for the times when you mess up your grand plan. Put a Gooball in the wrong place? Just click a timebug to go back a step. If your tower falls over completely, you can use a few timebugs to try and make some emergency repairs in time.
Build Quickly
There are a number of levels where you just need to build as fast as possible. I'm not just talking about the ones with a time limit either. Some structures tend to destabilize the longer you wait. Towers seem to sway more as the Gooballs climb and shift their weight. This can easily wreck your tower. On the other hand, bridges usually stop swaying over time. This can be disastrous when you are trying to catch onto an anchor point on the other side. That sway might just have given you enough height to latch onto the other side.
The Power of the Pipe
Another reason to build quickly is that the pipe's suction is quite strong. It is effectively another anchor point for your structure once you are within range. Your unstable tower is going to be just fine as long as you reach that pipe before it falls apart.