During an idle weekend moment ...
I took a list of library organizations -- Library of Congress, RLG, OCLC, Urban Libraries Council, CLIR, ARL, ALA, CNI, IMLS -- and did a 'find related' or 'find similar' search on them in Google (they use both related and similar for the same search). (Note: I didn't look at links.)
I then took the top ten results (following the number one result, which is always the seed website) for each, and noted the organization whose website it was. I gave each organization in this list a score, based on its rank in the result list, higher nearer the top. I then summed all the scores, and ended up with the following ranked list: ALA, RLG, LC, ARL, Internet Public Library, CNI, CLIR, Association of American Museums, British Library, Association of American Law Librarians, CILIP (UK equivalent to ALA), OCLC, SOLINET. There were many other organizations tailing off.
Now, I am not sure if this means anything, but it was interesting to do. Of the sites I started with, neither IMLS nor Urban Libraries Council came in any other organizations' top ten related. I counted LITA and PLA as ALA hits. ALA had much the highest score, maybe related to its involvement in a wide range of library activities. RLG was a long way behind ALA, but quite a bit ahead of LC. Not clear to me why that might happen.