The Collaborative International Dictionary of English v.0.48:

Arrogant \Ar"ro*gant\, a. [F. arrogant, L. arrogans, p. pr. of
   arrogare. See Arrogate.]
   1. Making, or having the disposition to make, exorbitant
      claims of rank or estimation; giving one's self an undue
      degree of importance; assuming; haughty; -- applied to
      persons.
      [1913 Webster]

            Arrogant Winchester, that haughty prelate. --Shak.
      [1913 Webster]

   2. Containing arrogance; marked with arrogance; proceeding
      from undue claims or self-importance; -- applied to
      things; as, arrogant pretensions or behavior.
      [1913 Webster]

   Syn: Magisterial; lordly; proud; assuming; overbearing;
        presumptuous; haughty. See Magisterial.
        [1913 Webster]

WordNet (r) 3.0 (2006):

arrogant
    adj 1: having or showing feelings of unwarranted importance out
           of overbearing pride; "an arrogant official"; "arrogant
           claims"; "chesty as a peacock" [syn: arrogant,
           chesty, self-important]