Although there are dozens I could list, here are just a few examples of some assumptions that could be mistakenly made as you look for your ancestors:
Assumption #1: When a spouse is no longer in a household, he or she must have died. Even though you may be looking at censuses from a century or more ago, couples did separate and divorce so keep digging for your ancestor in another home. My maternal 2nd great-grandparents appear to have been living separately for up to 20 years and died in different states.
Assumption #2: When an elderly ancestor can't be located in a census, he or she must have died. Even though life expectancy was lower in the 1900s, an ancestor who was in his 60s in one census and then can't be found in the next census doesn't necessarily mean that he/she died. I located my 3rd great-uncle James Baker in the 1920 census but am still looking for him in the 1930 and 1940 censuses. His Pennsylvania death certificate indicates that he didn't die until 1944, so an assumption that he died between 1920 and 1930 would have been wrong.
Assumption #3: An immigrant ancestor would not have returned to the old country. We've heard how difficult the trip across the Atlantic was for immigrants, so it would be easy to assume they never left North America after their arrival. My paternal 2nd great-grandfather returned to Germany in 1890, more than 35 years after leaving. On the PBS genealogy show, Finding Your Roots, one of Chef Tom Colicchio's ancestors made the trip back to Italy at least three times.
Assumption #4: A couple living together with children are the parents of those children. There used to be at least one Ancestry member tree that showed my 2nd great-aunt Christina Belsterling as the mother of my grandfather and his two siblings. She was their aunt, and they went to live with her after their mother died. Christina also was not the mother of the other children in the house; she was their stepmother.
Assumption #5: Your city laborer ancestor couldn't have owned several pieces of property. My 3rd great-grandfather Peter Klein was a coal miner. When I searched probate records, I really didn't expect to find a will for him. It seemed to be a trend in my family: no photos, no wills, no headstones. I just assumed my family was full of hardworking, but poor, laborers. But Peter did have a will, and it surprised me to read about his plan of 12 lots that he left to his wife and children. A map from 1896 shows it clearly marked as the "P. Klein Plan."
So remember, preliminary assumptions in genealogy research are ok as long as you look for the facts to determine if those assumptions are accurate.