(for accessibility they do not use DREs -- they chose either ballot-marking devices such as the Automark, or a system such as vote-by-phone such as the IVS Inspire):
AL, ID, MI, MN, MT, NE, NH, NM, ND, OK, OR, RI, SD, VT
(for accessibility some counties use DREs, others use ballot-markers):
AZ (primary voting system is OpScan; DREs are used in most counties for accessibility only; two or three counties use Automark)
IL (OpScan in most counties, some DREs for accessibility, some counties with Automark)
WY (20 counties use OpScan with Automark; 3 counties use DREs with VVPAT for accessibility only but OpScan is their primary voting system)
NC (76 out of 100 counties use OpScan)
AR, CA, IN, IA, KS, MS, MO, PA, TX, VA, WA, WV
3 States that will probably remain OpScan only, or will have DREs with a paper trail for accessibility only (purchases not yet complete):
MA, ME, WI
3 States still unknown (purchases not yet complete):
CT, NY, TN
As this list illustrates, OpScan is the most widely-used voting system in the United States. Despite increased use of DREs due to HAVA funding and the misunderstanding of some states soon after HAVA passed that HAVA required DREs, a number of states have increased their use of OpScan rather than decreased it, including North Carolina, California, Washington and perhaps others. For example, Buncombe County in North Carolina recently decided to sell its ES&S iVotronic DREs despite having just purchased them -- they used them in one election and decided to switch to the Automark paper-ballot-marker.
There are also some states or counties that use paper ballots that are hand-counted but the list has not been compiled yet.