CSV Import Isn't Working As Expected
One common problem is a CSV file that has a few commas between first and last names. Because the import is looking at commas as the delimiter it sees the fields with commas as two fields and doesn't know what to do with them. You can just remove the commas as I did in the attached version, or you can change the delimiter to another character and manually set that character on import.
Another thing to watch out for is that you import all individuals in one file (and make sure the import Contact Type is set to Individual). Then import all organizations separately, with the appropriate Contact Type.