You quite probably have the Google Toolbar.

At the right end of the toolbar there should be a small wrench (spanner if you're Brit).

Click the wrench (an icon for "Tools") or click the "down triangle" beside the wrench and select Options.

At the top of the menu that opens, uncheck the box beside "Suggest Searches as you type."

You should still be able to click the "down triangle" at the right of the search box to see suggestions, but they should stop opening as you type in the box.

John