A quick search of county collecting in google took me to wikipedia and these clubs as well:

http://en.wikipedia.org/wiki/County_collecting
http://www.mob-rule.com/counties/
http://www.extramilerclub.org/
http://groups.yahoo.com/group/countyhunt/

A nice site for tracking the counties you have visited is

http://counties.visitedmap.com

Click the "Create Account" tab to get started or just go to

http://counties.visitedmap.com/create.php

Are you counting Parish in LA too? Visiting those in Alaska would be a real challenge as a lot of those you wouldn't even be able to access with a vehicle.

I have never heard of a county collector - although I do have a friend that collects countries - she's up to 83 (but she's a traveler, not a tourist).

And as for counties - what does DC count as?

In 2006 I found a geocache in each of the 36 counties of Oregon.
I have been in all 3 counties of Delaware. I believe those are the only states that I have been in all of the counties.
If you become a geocacher, you can find a cache in each county you visit and get a nice map on your profile page to keep track.

Boroughs of Alaska, parishes of Louisiana, independent cities in multiple states, and the District of Columbia typically are counted as "county equivalents".

That's not true only for "county counters" – county maps prepared by the U.S. government, for example, follow that principle.

Hi everyone. (Before you ask, I do what my username says, over 300000 total miles!)
Yes, I do collect counties, and am on the mob-rule site as “naked_driver”. If you go there, you will see I have completed ten states plus DC, and as of October 14, 2011, can form a continuous column of counties from the Gulf to Canada (go from Louisiana north to Iowa, hop across the Mississippi to Wisconisn, and to from there to the U. P., which is where you hit the border). Remember, though, that the independent cities of Virginia count as counties also.
Apparently the visitedmap domain is either out of order or has been discontinued. I used “Naked Driver” there but the site does not come up (I tried unsuccesfully to ping it). (Too bad as I had made a number of maps to reflect my travels in various years as the site only allows so many colors per map.) (I want to find another such site to make more maps.)
Also, look for the highways I have clinched (driven on) here: http://cmap.m-plex.com/stat/region.php?u=barefoot_driver&c=usa&rg=all&du=mi&sort=ra
(they objected to the word “naked” in a username); I have not driven ouside the US.
Keep collecting!