The National Archives of the United Kingdom has a clickable map of the archives in the UK and a list of national archives across the world. By the way, there are 2,246 archive institutions in England alone.
As shown above, there are 1,206 special archives, 488 local archives, 300 university archives, 96 private archives, 81 national archives, and 75 business archives. Hmm. What would constitute a reasonably exhaustive search in England? Of course, not all these archives genealogically significant records but how do you know which ones don't? Here are some more interesting numbers.
The UK Archive search only lists 276 archives in the United States of America. However, there is a Wikipedia article entitled, "List of archives in the United States," that lists a few and then links to additional pages with more lists. Notable among archives in the United States is that of State of Georgia which was scheduled to be closed in 2012 and then remained open for another year by order of the Governor after public outcry from around the U.S. The Georgia State Archives was then transferred to the University System of Georgia. By the way, the Wikipedia article is out of date.
The Society of American Archivists has a webpage entitled, "Finding and Evaluating Archives."
Of course, if you are really interested in doing some reasonably exhaustive (and exhausting) research you should be using ArchiveGrid to search over 1,000 archival institutions.
The challenge for genealogists is that few archives have comprehensive catalogs of their holdings. In many cases, you will see entries such as the following, that list only the general contents of the papers and manuscripts in their collections:
This collection contains 21.25 linear feet of documents including the following:
The George S. Tanner papers (1912-1992) contain personal and family materials related to George Tanner, a teacher and historian. Included are correspondence, arranged chronologically and alphabetically; biographies and autobiographies; journals and family histories; financial and medical records; writings and speeches; newsletters and news clippings; programs and brochures; and materials relating to the Church of Jesus Christ of Latter-day Saints (LDS Church).There is no way to find out exactly what is contained in this collection short of visiting the University of Utah and spending time examining the 21+ feet of documents.
Here is another interesting example of collections in a national library.
Here are 9 private collections in the National Library of Australia. Here is a screenshot of the reference to one of those collections.
If you were searching for information about this person, could you find it in the National Library of Australia?
What is my point? There are more places to search for information than there is time in any one person's life to look. But by using the search capabilities of the internet, including, but certainly not limited to, Google searches, you can find some very surprising resources.