1) A man's wife or widow was the mother of his children.
A man's children could have been fathered by his wife (or widow), a previous or later wife, or even another woman. Parentage is one of those genealogical facts which should never be assumed.
2) If no marriage record is found, the children are probably illegitimate.
Early marriages were not always documented. Marriage records may have also been lost due to fire, water damage or neglect. The marriage may have been misfiled, or the record kept in a repository which you have not yet checked. When you can't find a marriage record, look for alternative forms of proof - including newspaper announcements and church records.
3) Three men living in the same county, who are close in age with the same last name, are probably brothers.
While this is an understandable assumption, these men could actually be cousins, or even unrelated. Look for further corroborating evidence, including the proximity of their homes, common naming patterns among their children, and records in which they are listed as witnesses for each other.
4) That an ancestor named Jr. has a father with the same name.
The terms "Junior" and "Senior" as well as other family terms such as "aunt" and "cousin" were often used very loosely. A designation of Jr., for example, may have been used in official records to identify between two men of the same name, even if they were unrelated (the younger of the two being called "Jr.").
5) People followed common migration routes.
Just because most of your ancestors' North Carolina neighbors came from Virginia, it doesn't mean that your ancestors did. While many individuals did follow common migration routes, making this a good working hypothesis, you can't assume it is true without further research.
6) People usually died in their sixties.
While most people in a generation may have followed the average life-span, your ancestor may have died very young from illness or accident, or lived to a much older age than many of their contemporaries. Just because your ancestor doesn't appear in the census after their 60th birthday doesn't necessarily mean that they died. Likewise, when a 20-year-old female no longer appears with her parents, it doesn't necessarily indicate that she must have married.
7) An ancestor who was born and died in the same place never moved.
It wasn't that uncommon for people to end up back where they started after spending a big part of their life moving around. Family, jobs or money may have caused your ancestors to move many times, but as these requirements lessened as they got older they may well have returned home to live near their family. Create a timeline for your ancestor's life and research their life and activities at many points along the way.
8) A female with the same last name as her father must be unmarried.
A common assumption to make, this genealogy premise often proves to be true. However, you need to rule out that the female didn't marry a man with the same surname as her father - a more common occurrence than you may think, especially in areas with a large number of families with the same surname. Alternatively, the daughter may actually have married, and then took back her father's name after a divorce.
9) That an ancestor who disappeared from the records of a town or county must have moved.
People aren't the only things that move. Political and geographical boundaries move as well. The county where your ancestor lived may have been divided into new counties, and his records may be found in a different courthouse. Or he may have started traveling to a courthouse in a a neighboring jurisdiction because a new road or other reason may have made that trip more convenient.
10) A male name indicates a male, and female name a female.
Names aren't always what they appear. Naming trends change often. The female first name Kimberly, for example, was originally a boy's name. Parents may also have chosen an unusual name to honor an ancestor, a famous individual, or just because they liked it.
While assumptions are a necessary part of genealogical research, the trick is to recognize them as assumptions, and substantiate or disprove them with further evidence. Avoiding false or mistaken assumptions can save hours of time and frustration.