Normally, there should be a little link to "Hide eBay suggestions" at the bottom right of the drop-down suggestion lists seen when you begin typing into the search bar.
If you use that link, the suggestions you should see should be the saved form data from previous searches that your browser keeps track of:
The little yellow box at the right side of the search field allows you to un-hide the eBay suggestions, if you want.
For a while, the hide/unhide options did not appear for me; I think the effect was not browser-dependent, but I am not entirely sure. Recently, the option has returned, for me at least.
