For example, let's assume a string 'green apple'. Is there at least one SE (or, maybe 3rd-party site) which provides its statistics on how often do users search this concrete string?
3 Answers
It's highly doubtful any engine will provide actual numbers for this information, but Google Trends does provide enough to get a feel for a term's recent performance. Whether that's useful will obviously depend upon how precise you really want this information to be.
You can also use the Google Adwords Tool
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+1 - Also worth mentioning: the Adwords tool offers Global and Local approximations which are particularly useful, as the results generated by the tool can be exported in a variety of formats for tracking over time. Sep 13, 2011 at 14:19
And here's another tool: Google Insights for Search
it helps you to compare search volume patterns across specific regions, categories, time frames and properties.