Try these steps in order:

  1. Make sure you're using the latest version of World of Goo (1.30). If you're not sure what version you have, just download and run the patch, it won't hurt anything. Note that, for a variety of good reasons, the demo version of the game is stuck at version 1.00.
  2. Download the latest, official video drivers from your manufacturer's website (not Windows Update). e.g. ATI, NVidia, Intel.
  3. Temporarily disable any anti-malware or firewall software. In particular, Threatfire and Look'n'stop are known to be buggy and interfere with World of Goo. In the case of Threatfire, you will need to actually uninstall it as disabling it is not enough.
  4. Try running the game and, as quickly as possible as it loads, press ALT+ENTER to force it into windowed mode.
  5. Try running the game and, as quickly as possible as it loads, press CTRL+SHIFT+ESCAPE to open the task manager. World of Goo should now be minimised on your task bar. Click on it to restore it.
  6. Try adjusting the refresh rate in C:\Program Files\WorldOfGoo\properties\config.txt to match one that is supported by your driver (although this problem should be fixed in recent World of Goo version).