The Collaborative International Dictionary of English v.0.48:

Republic \Re*pub"lic\ (r?-p?b"l?k), n. [F. r['e]publique, L.
   respublica commonwealth; res a thing, an affair + publicus,
   publica, public. See Real, a., and Public.]
   [1913 Webster]
   1. Common weal. [Obs.] --B. Jonson.
      [1913 Webster]

   2. A state in which the sovereign power resides in the whole
      body of the people, and is exercised by representatives
      elected by them; a commonwealth. Cf. Democracy, 2.
      [1913 Webster]

   Note: In some ancient states called republics the sovereign
         power was exercised by an hereditary aristocracy or a
         privileged few, constituting a government now
         distinctively called an aristocracy. In some there was
         a division of authority between an aristocracy and the
         whole body of the people except slaves. No existing
         republic recognizes an exclusive privilege of any class
         to govern, or tolerates the institution of slavery.
         [1913 Webster]

   Republic of letters, The collective body of literary or
      learned men.
      [1913 Webster]

WordNet (r) 3.0 (2006):

republic
    n 1: a political system in which the supreme power lies in a
         body of citizens who can elect people to represent them
         [syn: democracy, republic, commonwealth]
    2: a form of government whose head of state is not a monarch;
       "the head of state in a republic is usually a president"

The Devil's Dictionary (1881-1906):

REPUBLIC, n.  A nation in which, the thing governing and the thing
governed being the same, there is only a permitted authority to
enforce an optional obedience.  In a republic, the foundation of
public order is the ever lessening habit of submission inherited from
ancestors who, being truly governed, submitted because they had to.
There are as many kinds of republics as there are graduations between
the despotism whence they came and the anarchy whither they lead.