There are many private sector trash and recycling haulers for County residents to choose from:
http://www.fairfaxcounty.gov/dpwes/trash/disphaulers.htm
This link discusses how a group of homes and/or an HOA can petition the County to set up a new Sanitary District (Solid Waste Collection areas served by County trucks). There is an additional fee that is added to your tax bill to pay for the service. This County operation is known for doing a great job:
http://www.fairfaxcounty.gov/dpwes/trash/customer.htm