The Siren Board

Madison County, AL: 1st Wednesday of the month at noon, weather permitting.
Lauderdale County, AL: 1st and 3rd Wednesdays of the month at noon, weather permitting.

Pierce County, WA: First Monday of the month at noon, rain or shine.

Lincoln city, OR: Every single wednesday at 11. Most other Oregon coastal cities follow suit.

Every Virginia schedule I know:

Surry Power Station: Second Wednesday of March, June, September, and December at 11:10 AM. 3 minutes of alert.
North Anna Power Station: Third Wednesday of February, May, August, and November at 11:10 AM. 3 minutes of alert.
Virginia Commonwealth University: First Wednesday of the month at 12 PM. 1 minute of alert, though apparently they run a "full test" every so often that involves 3 minutes of fast wail followed by said minute of alert.
Christopher Newport University: Whenever they feel like it. Supposedly "every few weeks", but I've only heard the system test 4 or 5 times since it was installed (including the 2014 tornado drill). Alert blast bookended by voice messages. *
Jefferson Lab: First Friday of the month at 10:30 AM. 30 seconds to 3 minutes of 10-4 attack. *
University of Richmond: Once a semester; dates are announced in advance. Was first Monday of the month at 1:25 PM until 7/7/2014. *
Langley AFB: No regular siren testing AFAIK, but they do run music every weekday at 6 AM, 12 PM, and 5 PM.
Old Dominion University: No regular testing AFAIK. *
City of Martinsville: Their new system of 16V1T-Bs will test "once or twice a month" once it is installed.
Galax VFD: Saturdays at noon.
Newport News Shipyard: No testing per se, but their Model 5 sounds alert blasts every workday to signal lunch breaks, shift changes, etc.
City of Blackstone: Every first Wednesday of the month at 6 PM. *
Town of Abingdon: Uncertain, but... *
Town of Warrenton: As far as I am aware, Saturdays at noon. *

* Runs siren(s) for the statewide tornado drill in March.

Plus a couple of others:

Pennington County, SD: 1st and 3rd Saturdays at noon.
Campbell County, WY: 2nd Tuesday of the month. Wright tests at 8:15 AM, Gillette at 10:30 AM.
Sheffield, IL: Noon blast daily.

Macomb County, MI:Sirens test on 1st Saturday of the month at 1 PM.

Talladega County, AL: first Tuesday of the month at 4:00 PM, weather permitting. Make-up day is the following Thursday at 10:00 AM, weather permitting.

Active:
Almost everywhere in Atlanta: First wednesday at 12:00 hrs
Bibb Co.: Last Wednesday at 10:00 or 11:00 hrs (Ian please confirm)
Jefferson Co. AL: 1st wednesday at 10:00 Hrs.
Anderson Co, SC: Every Friday at 18:00 Hrs. (A few exceptions)
Spartanburg County, SC: First Saturday at 13:00 hrs.
Laurens Co, SC: Every Saturday at 12:00 hrs.
Newberry Co, SC: Every Saturday at 12:00 hrs. (Exception being one Thunderbolt which is tested yearly)
Rhine, GA: Every Saturday at 12:00 Hrs.
Houston Co, GA: Third saturday at 12:00 Hrs.


Inactive:
Greenville, SC tested their Chrysler every saturday at 12:00 hours if I am not mistaken.
DeKalb County, GA (Pre-1989) First wednesday at 12:00 hrs. SHARP
Atlanta, GA (Pre-1986): Every Friday at 12:00 Hrs

These are all of the ones I can remember off the top of my head. At least I got to brush up on my knowledge of 24 hour time.

I know Boone County was in the first post, but they not only test every first Wednesday at noon but they do short blasts the rest of the Wednesdays at noon as well, weather permitting.