Helligkorsgade, Kølding, DK (built 1589; photo from WikimediaCommons by User:Mahlum, 2006)
Danish Demes
a Regional DNA Project for Danish Americans and Danes around the World
Borches gård, Kolding, DK (built 1595; photo from WikimediaCommons by User:Mahlum, 2006)
 
Links Hub for Native-Born Danes and Their Relatives
in the Censuses of the United States and Canada
 
Below is my attempt at extracting all households from the censuses of the United States and Canada containing individuals giving Denmark as their birthplace.  Such extractions are only possible from 1850 onwards in the U.S. and 1851 onwards in Canada because those were the first enumerations to begin including the names and birthplaces of individuals in the household. 

Constitutionally mandated decennial censuses began in the United States in 1790, and the most recently released U.S. census is 1930.  Canada did not become a nation until 1867, so mandated decennial censuses did not begin there until 1871, however territorial censuses began 1851.  The most recently released Canadian census is 1911.

There were numerous other censuses in both countries, beyond the nationwide decennial ones.  I will include these other censuses as available, but priority is being given to extracting the decennial ones, first.
 
Census Timeline Tables
Canada
AB BC MB NB NL NT NS ON PE QC SK YT
United States
AL AK AZ AR CA CO CT DE FL GA HA ID
IL IN IA KS KY LA ME MD MA MI MN MS
MO MT NE NV NH NJ NM NY NC ND OH OK
OR PA RI SC SD TN TX UT VT VA WA WV
WI WY District of Columbia
 
Census Record Tables

Years in bold font are completed. Years without links have not been started.
Empty cells indicate no census was taken (or is not available at Ancestry.com). Gray cells indicate census was lost.
Years in small text indicate there were no individuals giving Denmark as their birthplace in the census in that year in that state or province.
 
Canadian Provinces
NB             1851  1861 1871 1881 1891 1901 1911     NB
NS             1851 1861 1871 1881 1891 1901 1911     NS
ON             1851 1861 1871 1881 1891 1901 1911     ON
QC             1851 1861 1871 1881 1891 1901 1911     QC
PE               1861   1881 1891 1901 1911     PE
BC                   1881 1891 1901 1911     BC
MB                   1881 1891 1901 1911     MB
NT                   1881 1891 1901 1911     NT
YT                        1901 1911     YT 
AB                         1911     AB
SK                         1911     SK
NL                               NL
 
New England States
ME 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 ME
NH 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 NH
VT 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 VT
MA 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 MA
CT 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 CT
RI 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 RI
 
Northern Tier of States
NY 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 NY
MI       1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 MI
WI           1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 WI
IA           1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 IA
MN             1850 1860 1870 1880 1890 1900 1910 1920 1930 MN
 
Middle Tier of States
NJ 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 NJ
PA 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 PA
OH     1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 OH
IN       1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 IN
IL       1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 IL
MO         1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 MO
 
DC 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 DC
 
Southern States
DE 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 DE
MD 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 MD
VA 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 VA
WV 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 WV
NC 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 NC
SC 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 SC
GA 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 GA
KY   1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 KY
TN   1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 TN
LA     1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 LA
MS       1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 MS
AL       1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 AL
AR         1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 AR
FL         1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 FL
Although WV did not become a state until 1863, I'm treating its counties as if the state had existed from the start.
For Tennessee, all but one county was lost in 1810, and in 1820, 22 of the then existing 48 counties were lost.
Western, Southwestern, and Great Plains States
TX             1850 1860 1870 1880 1890 1900 1910 1920 1930 TX
UT             1850 1860 1870 1880 1890 1900 1910 1920 1930 UT
NM             1850 1860 1870 1880 1890 1900 1910 1920 1930 NM
CA             1850 1860 1870 1880 1890 1900 1910 1920 1930 CA
OR             1850 1860 1870 1880 1890 1900 1910 1920 1930 OR
WA               1860 1870 1880 1890 1900 1910 1920 1930 WA
KS               1860 1870 1880 1890 1900 1910 1920 1930 KS
NE               1860 1870 1880 1890 1900 1910 1920 1930 NE
DT               1860 1870 1880 1890 1900 1910 1920 1930 ND
1890 1900 1910 1920 1930 SD
AZ               1860 1870 1880 1890 1900 1910 1920 1930 AZ
NV                 1870 1880 1890 1900 1910 1920 1930 NV
ID                 1870 1880 1890 1900 1910 1920 1930 ID
MT                 1870 1880 1890 1900 1910 1920 1930 MT
CO                 1870 1880 1890 1900 1910 1920 1930 CO
WY                   1880 1890 1900 1910 1920 1930 WY
OK                     1890 1900 1910 1920 1930 OK
AK                     1890 1900 1910 1920 1930 AK
HA                     1890 1900 1910 1920 1930 HA
PLEASE NOTE:  The purpose of the Census Record Tables is for them to function as an every- name index to the census.  The extractions given in the Census Record Tables are not intended as a substitute for seeking out the original record because 1) these extraction's do not necessarily include all non-Danish individuals in the household, and 2) these extractions are not entirely verbatim.  To facilitate computerized searching, the spelling of names and places has been standardized and corrected, regardless of how the names or locations were spelled in the original record.  Where there is a link to the householder, this link will lead to a family group sheet that will contain a complete, verbatim extraction of the census record, plus whatever additional information I have on the family.  The only instance when the extractions on the family group sheets may not be verbatim is for the birth location, where I will sometimes use an abbreviation to save space (e.g., PA for Pennsylvania, Ger for Germany, DK for Denmark, etc.), I only use three letters to abbreviate the month, and I always abbreviate "Daughter" as "Dau," "Grandson" as "GSon," etc.  For all records, I have supplied enough information so the original record can be readily retrieved from the usual sources.

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Memorial stone for King Erik I (c1060-1103), a.k.a., 'Erik the Good' or Erik Ejegod; Borgvold, Viborg Amt, DK (photo from WikimediaCommons by User:Calvin, 2007). Viking burial ground (700-1150 CE), Lindholm Høje, Aalborg Amt, DK (photo from WikimediaCommons by User:Bunnyfrosch, 2007).