The Collaborative International Dictionary of English v.0.48:

Adder \Ad"der\, n. [OE. addere, naddere, eddre, AS. n[ae]dre,
   adder, snake; akin to OS. nadra, OHG. natra, natara, Ger.
   natter, Goth. nadrs, Icel. na[eth]r, masc., na[eth]ra, fem.:
   cf. W. neidr, Gorn. naddyr, Ir. nathair, L. natrix, water
   snake. An adder is for a nadder.]
   1. A serpent. [Obs.] "The eddre seide to the woman."
      --Wyclif. Gen. iii. 4. )
      [1913 Webster]

   2. (Zool.)
      (a) A small venomous serpent of the genus Vipera. The
          common European adder is the Vipera berus or Pelias
          berus. The puff adders of Africa are species of
          Clotho.
      (b) In America, the term is commonly applied to several
          harmless snakes, as the milk adder, puffing adder,
          etc.
      (c) Same as Sea Adder.
          [1913 Webster]

   Note: In the sculptures the appellation is given to several
         venomous serpents, -- sometimes to the horned viper
         (Cerastles).
         [1913 Webster]

WordNet (r) 3.0 (2006):

Vipera berus
    n 1: small terrestrial viper common in northern Eurasia [syn:
         adder, common viper, Vipera berus]