The Collaborative International Dictionary of English v.0.48:

Assess \As*sess"\, v. t. [imp. & p. p. Assessed; p. pr. & vb.
   n. Assessing.] [OF. assesser to regulate, settle, LL.
   assessare to value for taxation, fr. L. assidere, supine as
   if assessum, to sit by, esp. of judges in a court, in LL. to
   assess, tax. Cf. Assize, v., Cess.]
   1. To value; to make a valuation or official estimate of for
      the purpose of taxation.
      [1913 Webster]

   2. To apportion a sum to be paid by (a person, a community,
      or an estate), in the nature of a tax, fine, etc.; to
      impose a tax upon (a person, an estate, or an income)
      according to a rate or apportionment.
      [1913 Webster]

   3. To determine and impose a tax or fine upon (a person,
      community, estate, or income); to tax; as, the club
      assessed each member twenty-five cents.
      [1913 Webster]

   4. To fix or determine the rate or amount of.
      [1913 Webster]

            This sum is assessed and raised upon individuals by
            commissioners in the act.             --Blackstone.
      [1913 Webster]

WordNet (r) 3.0 (2006):

assess
    v 1: evaluate or estimate the nature, quality, ability, extent,
         or significance of; "I will have the family jewels
         appraised by a professional"; "access all the factors when
         taking a risk" [syn: measure, evaluate, valuate,
         assess, appraise, value]
    2: charge (a person or a property) with a payment, such as a tax
       or a fine
    3: set or determine the amount of (a payment such as a fine)
       [syn: tax, assess]
    4: estimate the value of (property) for taxation; "Our house
       hasn't been assessed in years"

Moby Thesaurus II by Grady Ward, 1.0:

81 Moby Thesaurus words for "assess":
   account, appraise, appreciate, ask, assay, calculate, calibrate,
   caliper, call, catalog, categorize, charge, charge for,
   check a parameter, class, classify, compute, consider, deem,
   demand, dial, divide, estimate, evaluate, exact, factor,
   fair-trade, fathom, figure, form an estimate, gauge,
   give an appreciation, graduate, group, guess, identify, impose,
   levy, make an estimation, make dutiable, mark, measure, mensurate,
   mete, meter, pace, plumb, price, prize, pro rata, probe, prorate,
   put, quantify, quantize, quote a price, rank, rate, reckon,
   require, set at, sift, size, size up, sort, sort out, sound, span,
   step, stick for, survey, take a reading, tax, thrash out, tithe,
   triangulate, valorize, valuate, value, weigh, winnow