Opensearch specification has extension for search suggestions. Major search providers have their own search suggestion entry points. After looking doing a search of my own, I found the entry points for the 3 major search providers

Bing –{Search Term}
Google –{Search Term}&client=firefox
Yahoo –{searchTerms}

For Google entry point, removing client parameter will also provide the number of results in the response. This format is not as per the Opensearch standards.