WordNet (r) 3.0 (2006):

go after
    v 1: go after with the intent to catch; "The policeman chased
         the mugger down the alley"; "the dog chased the rabbit"
         [syn: chase, chase after, trail, tail, tag, give
         chase, dog, go after, track]
    2: go in search of or hunt for; "pursue a hobby" [syn: quest
       for, go after, quest after, pursue]

Moby Thesaurus II by Grady Ward, 1.0:

69 Moby Thesaurus words for "go after":
   attend, bedog, bring, bring back, c, call for, chase, chase after,
   chivy, come after, come behind, come on, displace, dog, emanate,
   ensue, fetch, fetch and carry, follow, follow after, follow up,
   get, give chase, go and get, go behind, go fetch, go for, go get,
   go to get, heel, hollo after, hound, hunt, inherit, issue,
   make after, move behind, obtain, overtake, pick up, procure,
   prosecute, pursue, quest, quest after, raise the hunt, replace,
   result, retrieve, run after, search, secure, seek, seek out,
   shadow, shag, string along, succeed, supervene, tag, tag after,
   tag along, tail, tailgate, take out after, track, trail,
   trail after, tread close upon