The assumption that people who marry their cousins must be hillbillies from remote and uncivilized areas is far from accurate. True, there are fewer states which allow first cousin marriage, but ironically, it is the more populated and industrialized states which accept such unions.

To the left of some states you will see the following notes:

Age: State allows first cousin marriage only if the couple is beyond childbearing age or otherwise unable to have children.
GC: State allows first cousins to marry, but requires genetic counseling prior to obtaining license.
DF: State allows all first cousins to marry except those who are related on both maternal and paternal sides (Double First Cousins)
xR: Laws also apply to first cousins once removed.
Summary of results:
More than 57% of American citizens who can not have children can marry a cousin if they choose.
More than 52% of all American citizens may marry a cousin if they choose, with no restrictions.
 
2000 Census Bureau Demographics
States that allow cousin marriage States that prohibit cousin marriages
Some Restrictions may apply  Population Population
Alabama 4,447,100 Arkansas 2,673,400
Alaska 626,932 Delaware 783,600
*Age Arizona  5,130,632 Idaho 1,293,953
California 33,871,648 Iowa 2,926,324
Colorado 4,301,261 Kansas 2,688,418
Connecticut 3,405,565
*xR 
Kentucky  4,041,769
DC 572,059 Louisiana 4,468,976
Florida 15,982,378 Michigan 9,938,444
Georgia 8,186,453 Minnesota 4,919,479
Hawaii 1,211,537 Mississippi 2,844,658
*Age Illinois  12,419,293 Missouri 5,595,211
*Age, xR Indiana  6,080,485 Montana 902,195
*GC Maine  1,274,923 Nebraska 1,711,263
Maryland 5,296,486
*xR 
Nevada  1,998,257
Massachusetts 6,349,097 New Hampshire 1,235,786
New Jersey 8,414,350 North Dakota 642,200
New Mexico 1,515,069
    *xR 
Ohio  11,353,140
New York 18,976,457 Oklahoma 3,450,654
*DF North Carolina  8,049,313 Oregon 3,421,399
Rhode Island 1,048,319 Pennsylvania 12,281,054
South Carolina 4,012,012 South Dakota 754,844
Tennessee 5,689,283
*xR 
Washington  5,894,121
Texas 20,851,820 West Virginia 1,808,344
*Age Utah  2,223,169 Wyoming 493,782
Vermont 608,827
Virginia 7,078,515
*Age, xR Wisconsin  5,363,675
Total 161,722,409. Total 88,121,271
% of total  57.5% % of total 31.3%
US Population 2000 281,421,906 
States that allow cousin marriage States that prohibit cousin marriages
No age or infertility restrictions  Population Population
Alabama 4,447,100 Arkansas 2,673,400
Alaska 626,932 Delaware 783,600
California 33,871,648 Idaho 1,293,953
Colorado 4,301,261 Iowa 2,926,324
Connecticut 3,405,565 Kansas 2,688,418
DC 572,059
*xR 
Kentucky  4,041,769
Florida 15,982,378 Louisiana 4,468,976
Georgia 8,186,453 Michigan 9,938,444
Hawaii 1,211,537 Minnesota 4,919,479
*GC Maine  1,227,928 Mississippi 2,844,658
Maryland 5,296,486 Missouri 5,595,211
Massachusetts 6,349,097 Montana 902,195
New Jersey 8,414,350 Nebraska 1,711,263
New Mexico 1,515,069 Nevada  1,998,257
New York 18,976,457 New Hampshire 1,235,786
*DF North Carolina  8,049,313 North Dakota 642,200
Rhode Island 1,048,319
*xR 
Ohio  11,353,140
South Carolina 4,012,012 Oklahoma 3,145,585
Tennessee 5,689,283 Oregon 3,421,399
Texas 20,851,820 Pennsylvania 12,281,054
Vermont 608,827 South Dakota 754,844
Virginia 7,078,515
*xR 
Washington  4,866,692
West Virginia 1,808,344
Wyoming 493,782
*Age, xR 
Arizona  5,130,632
Illinois  12,419,293
*Age, xR 
Indiana  6,080,485
  *Age 
Utah  2,223,169
*Age, xR 
Wisconsin  5,363,675
Total 130,505,155. Total 119,338,525
% of total  52.5% % of total 47.9%
US Population 2000 281,421,906