In Fairfax County, VA, if a subpoena for a deposition is to be served
regarding a civil case, how must the subpoena be delivered? i.e., does
it have to be handed to me? Can it be slid under my door? Left on my
windshield? Can I dodge it?

What is a subpoena?
an order of a court which requires a person to be present at a certain
time and place or suffer a penalty (subpoena means, literally, "under
penalty"). This is the traditional tool used by lawyers to ensure that
witnesses present themselves at a given place, date and time to make
themselves available to testify

http://serveitnow.com/process-server/Virginia/Fairfax-County/

Rules for delivery of subpoena's in Fairfax
http://www.fairfaxcounty.gov/courts/circuit/pdf/CCR-A-248.pdf
Counsel will mail the "original" Attorney Issued Subpoena and one copy for each
person being served to the Sheriff or Private Process Server. If
service by Sheriff, must include a Sheriff Transmittal Sheet with the
subpoena.


So no you can not dodge a subpoena, as it can be just mailed to you.

Actually it doesn't say that it can be mailed to you, just that the
copies can be mailed.

Here is a more relevant quote;
http://www.law.pitt.edu/wasserman/law6e.htm#N_152_

Consolidation Coal Co. v. Local 1784, 514 F.2d 763, 765-66 (6th Cir.
1975) holding that personal service of motion for contempt hearing or
order to show cause was not required where workers allegedly were
violating a no-strike injunction, but some notice of the hearing was
required.

From those sites, it seems that in Elids-ga's 1st comment that was
referring to delivery of the subpoena to the sheriff or server, and
perhaps to delivery of confirmation of the "serving" of the subpoena. 
The fact that a the sheriff or a "server" (a whole service industry
from the first site) is necessary, suggests that mailin or just
delivering to the last known address is inadequate.