Starting in 1790, the United States government took a census every 10 years. Census information exists for the 1900, 1910, 1920, and 1930 census for Alaska. Unfortunately, earlier census enumerations (1880-1890) did not survive. Even though Alaska was purchased in 1867, there was no 1870 census taken.
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Ronald Vern Jackson wrote a book in 1976 (currently out of print) that went into depth about the Alaska State census 1870-1907. The information from this book which will prove invaluable to Alaskan researchers, can be found online at Ancestry. I have not found any of this information online for free yet. Alaska Census 1870-1907 (must have Ancestry membership to view information, but search is free).
Following census are hosted at Alaska USGenWeb Archives