If you need to get Google search result count for some query, using estimatedResultCount from Google AJAX Search API sounds like a winner. However, the number reported as estimatedResultCount doesn’t match the number displayed on regular search pages and could be different in many times. This is known issue since 2008 and it seems it will never be fixed.
So if you want more correct result count, the extract it from regular Google search page. Alternatively you can use Yahoo or Bing APIs as they report the same numbers to displayed on their regular search pages.
UPDATE: It was found that regular Google search pages display even more rough estimated result count than Google AJAX Search API. For example, query for "pumka.net" (w/ quotes) it reports "About 1,380 results" while only finds 284 pages. Bing reports 55 results while finds 50-52 and Yahoo reports 210 results while finds 55. So using Bing or Yahoo API for analysis of result counts is likely more accurate.