The Collaborative International Dictionary of English v.0.48:

Birthright \Birth"right`\, n.
   Any right, privilege, or possession to which a person is
   entitled by birth, such as an estate descendible by law to an
   heir, or civil liberty under a free constitution; esp. the
   rights or inheritance of the first born.
   [1913 Webster]

         Lest there be any . . . profane person, as Esau, who
         for one morsel of meat sold his birthright. --Heb. xii.
                                                  16.
   [1913 Webster]

WordNet (r) 3.0 (2006):

birthright
    n 1: a right or privilege that you are entitled to at birth;
         "free public education is the birthright of every American
         child"
    2: an inheritance coming by right of birth (especially by
       primogeniture) [syn: birthright, patrimony]
    3: personal characteristics that are inherited at birth

Moby Thesaurus II by Grady Ward, 1.0:

52 Moby Thesaurus words for "birthright":
   appanage, appurtenance, authority, bequeathal, bequest,
   borough-English, claim, coheirship, conjugal right, coparcenary,
   demand, divine right, droit, due, entail, faculty, gavelkind,
   heirloom, heirship, hereditament, heritable, heritage, heritance,
   inalienable right, incorporeal hereditament, inheritance, interest,
   law of succession, legacy, line of succession, mode of succession,
   natural right, patrimony, perquisite, postremogeniture, power,
   prerogative, prescription, presumptive right, pretense, pretension,
   primogeniture, privilege, proper claim, property right, reversion,
   right, succession, title, ultimogeniture, vested interest,
   vested right



Easton's 1897 Bible Dictionary:

Birthright
   (1.) This word denotes the special privileges and advantages
   belonging to the first-born son among the Jews. He became the
   priest of the family. Thus Reuben was the first-born of the
   patriarchs, and so the priesthood of the tribes belonged to him.
   That honour was, however, transferred by God from Reuben to Levi
   (Num. 3:12, 13; 8:18).

     (2.) The first-born son had allotted to him also a double
   portion of the paternal inheritance (Deut. 21:15-17). Reuben
   was, because of his undutiful conduct, deprived of his
   birth-right (Gen. 49:4; 1 Chr. 5:1). Esau transferred his
   birth-right to Jacob (Gen. 25:33).

     (3.) The first-born inherited the judicial authority of his
   father, whatever it might be (2 Chr. 21:3). By divine
   appointment, however, David excluded Adonijah in favour of
   Solomon.

     (4.) The Jews attached a sacred importance to the rank of
   "first-born" and "first-begotten" as applied to the Messiah
   (Rom. 8:29; Col. 1:18; Heb. 1:4-6). As first-born he has an
   inheritance superior to his brethren, and is the alone true
   priest.