Zero no Tsukaima is the absolute best example of this. Louise called "The Zero Louise" by her classmates due to her inability to effectively use magic despite coming from a very well known magical family is in her second year of the magic academy that she attends. Second years are required to undergo a ceremony to summon a 'familiar' that they will stay with the rest of their life. A familiar ranges throughout a variety of magical creatures and beings. Among those, the lowest familiar is regarded as a "plebian" or a creature that cannot use magic.