The Collaborative International Dictionary of English v.0.48:

Pursue \Pur*sue"\, v. i.
   1. To go in pursuit; to follow.
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            The wicked flee when no man pursueth. --Prov.
                                                  xxviii. 1.
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            Men hotly pursued after the objects of their
            ambition.                             --Earle.
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   2. To go on; to proceed, especially in argument or discourse;
      to continue.
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   Note: [A Gallicism]
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               I have, pursues Carneades, wondered chemists
               should not consider.               --Boyle.
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   3. (Law) To follow a matter judicially, as a complaining
      party; to act as a prosecutor. --Burrill.
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The Collaborative International Dictionary of English v.0.48:

Pursue \Pur*sue"\, v. t. [imp. & p. p. Pursued; p. pr. & vb.
   n. Pursuing.] [OE. pursuen, porsuen, OF. porsivre,
   poursuivre, poursuir, F. poursuivre, fr. L. prosequi; pro
   forward + sequi to follow. See Sue, and cf. Prosecute,
   Pursuivant.]
   1. To follow with a view to overtake; to follow eagerly, or
      with haste; to chase; as, to pursue a hare.
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            We happiness pursue; we fly from pain. --Prior.
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            The happiness of men lies in purswing,
            Not in possessing.                    --Longfellow.
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   2. To seek; to use or adopt measures to obtain; as, to pursue
      a remedy at law.
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            The fame of ancient matrons you pursue. --Dryden.
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   3. To proceed along, with a view to some and or object; to
      follow; to go in; as, Captain Cook pursued a new route;
      the administration pursued a wise course.
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   4. To prosecute; to be engaged in; to continue. " Insatiate
      to pursue vain war." --Milton.
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   5. To follow as an example; to imitate.
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   6. To follow with enmity; to persecute; to call to account.
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            The servant is not greater than his lord. If they
            have pursued me, they shall pursue you also.
                                                  --Wyclif (John
                                                  xv. 20).
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   Syn: To follow; chase; seek; persist. See Follow.
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WordNet (r) 3.0 (2006):

pursue
    v 1: carry out or participate in an activity; be involved in;
         "She pursued many activities"; "They engaged in a
         discussion" [syn: prosecute, engage, pursue]
    2: follow in or as if in pursuit; "The police car pursued the
       suspected attacker"; "Her bad deed followed her and haunted
       her dreams all her life" [syn: pursue, follow]
    3: go in search of or hunt for; "pursue a hobby" [syn: quest
       for, go after, quest after, pursue]
    4: carry further or advance; "Can you act on this matter soon?"
       [syn: pursue, follow up on, act on]

Moby Thesaurus II by Grady Ward, 1.0:

128 Moby Thesaurus words for "pursue":
   address, adhere to, angle for, ask for, aspire to, badger, bait,
   be into, be strong in, beat about for, beau, bedog, beset,
   carry on, chase, chase after, chevy, chivy, come after,
   come behind, conduct, confine, continue, court, cultivate,
   delve for, dig for, do, dog, employ, engage in, esquire, exercise,
   feature, fish for, follow, follow up, give chase, go after,
   go behind, go gunning for, go in for, gun for, harass, harry, heel,
   hollo after, hound, hunt, hunt for, hunt up, lay siege to, limit,
   look, look for, look up, maintain, major in, make after,
   make suit to, make up to, minor in, molest, move behind, narrow,
   oppress, pay attention to, pay court to, persecute, persevere,
   persist, persist in, practice, proceed with, prosecute,
   prowl after, purpose, quest, quest after, raise the hunt, restrict,
   ride, run after, run down, search, search for, see to, seek,
   seek for, seek out, serenade, shadow, spark, specialize,
   specialize in, squire, stalk, still-hunt, string along, strive for,
   sue, swain, sweetheart, tackle, tag, tag after, tag along, tail,
   tailgate, take on, take out after, take to, take up, torment,
   trace, track, trail, trail after, tread close upon, try for,
   try to find, undertake, use, victimize, wage, woo, work at,
   work for