I'm considering building my own vehicle from scratch, not from a kit. 
I need to know the requirements, and process for obtaining a vehicle
title in the state of Virginia for a self-assembled vehicle.  As part
of the requirements, I obviously would also need to know what safety
requirements would need to be satisfied to obtain a title.

Phooka,
Safety Requirements:  check out this site.  You can click your way through.

http://www.nhtsa.dot.gov/cars/testing/ncap/pages/ResourcesLinksNSSandR.htm

I couldn't find it  - didn't look long enough -  but I have a strong
suspicion that crash testing is required  - not so good for your
one-off baby.
I don't doubt that you can build a vehicle that drives and may be safe
for you and others, but I suspect that the safety requirements are so
intricate and detailed that they would defeat you.
Just a minor example from Europe:  now cars must have headlights that
can be tilted to compensate for heavy rear loading (not that people
remember to do so, or maybe even know what the little thumbwheel on
the dashboard is for).

Sorry to be so discouraging,
regard, Myoarin

I know for a fact that crash testing is not required.  There are a
good number of people that have accomplished this feat before.  There
are plenty of other resources for states other than Virginia.  Regular
kit cars do not endure crash testing either, because they aren't
completed by the manufacturer.  If a car is completely built by a
manufacturer, it must indeed have crash testing.  I'm not a
manufacturer :)

Well, I am glad that I was wrong about that.  :)
Myoarin

This is what I obtained from DMV

Once the vehicle has been built the following needs to be submitted to
Virginia DMV.

EVIDENCE OF OWNERSHIP

*Title for the frame
*Bill of sale for the body
*Bill of Sale for the engine
*Statement of how the vehicle was constructed (notarized)
*Picture of the road ready vehicle upon completion

FORMS

VSA22 - "App. for Assigned Vehicle ID#"
http://www.dmvnow.com/webdoc/pdf/vsa22.pdf

VSA17A - "App. for Certificate of Title and Registration"
http://www.dmvnow.com/webdoc/pdf/vsa17a.pdf

FEES
$5.00 for VIN Plate
$10.00 Titling fee
$35.00 Minimum Sales and Use tax
$29.50 Minimum Registration fee

Your vehicle, once complete also needs to be inspected by a Virginia
DMV inspector. The cost for this inspection is $25.00.

For specific information on height limits, and other safety equipment
regulations, you would need to contact the state police, who regulate
the state safety inspections. They can be reached through their web
site at www.vsp.state.va.us or by telephone at 800-552-9965.

Well, there you go. Sounds easy, but I'd check out all those
requirements before you start: DMV and the State Police.  You might
have to go through your plans with them.  I would, but I'm and old
Volvo driver and wouldn't think of building my own vehicle.  :)
Myoarin