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.
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   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.
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   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.
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   4. To fix or determine the rate or amount of.
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            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"