(Left: Example LiveSearch at alltheweb)
According to Yahoo, "Livesearch is a product that analyzes your search in real-time and instantly provides Web results with alternate search queries as you type. These suggested queries are based on what other people have searched for."
It is a lot like Google Suggest, but then it also has a kind of clustering effect, and Google Suggest just suggests queries, it doesn't actually run them.
More at Resource Shelf