Off-center coins are one of the most common and best known types of errors. This happens when a blank, as it is fed into the press, lands in the collar improperly. When this occurs only part of the blank is between the upper and lower dies. When the dies strike the blank, only that part will be struck with a design.

Images courtesy of Byers Numismatic Corp

Significant examples:
SBA $1 Struck 50% Off-Center (illustrated above).

1899 Indian Cent Struck 35% Off-Center.  NGC MS-65 Brown.  Ex – American Numismatic Rarities, LLC’s “The Classics Sale,” July 25, 2003 , Lot 600, "Snow-1", illustrated, sold for $1,150.00

Sources and/or recommended reading: