Google is currently testing Google Suggest on its homepage. Google Suggest provides Google's users with search suggestions as they type information within the search box.
Google Suggest was first seen around December 2004 and does not base its suggestions on your personal search history at the moment. Rather Google Suggest uses data regarding the popularity of various search terms in order to assist in providing users with search suggestions.
The image below is an example of Google's suggested search terms when you type "ipow" - the first for letters of IPOWERWEB.
Both Yahoo and Ask.com provide search suggestions by default. It will be interesting to see if Google will keep providing Google Suggest on its homepage.