The Collaborative International Dictionary of English v.0.48:

Maxim \Max"im\, n. [F. maxime, L. maxima (sc. sententia), the
   greatest sentence, proposition, or axiom, i. e., of the
   greatest weight or authority, fem. fr. maximus greatest,
   superl. of magnus great. See Magnitude, and cf. Maximum.]
   [1913 Webster]
   1. An established principle or proposition; a condensed
      proposition of important practical truth; an axiom of
      practical wisdom; an adage; a proverb; an aphorism.
      [1913 Webster]

            'T is their maxim, Love is love's reward. --Dryden.
      [1913 Webster]

   2. (Mus.) The longest note formerly used, equal to two longs,
      or four breves; a large.
      [1913 Webster]

   Syn: Axiom; aphorism; apothegm; adage; proverb; saying. See
        Axiom.
        [1913 Webster]

Moby Thesaurus II by Grady Ward, 1.0:

68 Moby Thesaurus words for "maxim":
   Procrustean law, a belief, adage, aphorism, apophthegm, apothegm,
   article of faith, axiom, brocard, byword, canon, cliche, code,
   commandment, commonplace, convention, criterion, dictum, doctrine,
   dogma, epigram, form, formality, formula, formulary,
   general principle, gnome, golden rule, guideline,
   guiding principle, imperative, law, law of nature, mitzvah, moral,
   mot, motto, norm, norma, order of nature, ordinance, platitude,
   precept, prescribed form, prescript, prescription, principium,
   principle, proverb, regulation, rubric, rule, rule of thumb, saw,
   saying, set form, settled principle, slogan, standard,
   standing order, teaching, tenet, theorem, truism, universal law,
   witticism, working principle, working rule