Can I run copper wire to a subpanel via the crawl space without conduit?
From the 2011 NEC 310.15(B)(7) table.
A 100 amp residential panel only requires #4 copper or #2 aluminum.
3/0 copper would be a waste of money. 

If you use SE cable you will need 3 insulated conductors along with the bare wire. 


  338.10(B)(2) Use of Uninsulated Conductor. Type SE service-entrance cable shall be permitted for use where the insulated conductors are used for circuit wiring and the uninsulated conductor is used only for equipment grounding purposes.


Since you a using it for a feeder to a sub-panel you have to have an insulated neutral and use the bare for the equipment ground.

Do not bond the neutral and ground in the sub-panel and keep the neutrals and grounds separated. You need a panel that is "suitable for use as service equipment" since it will have an insulated neutral bar. Discard the green bonding screw.

Happy Friday!