The Collaborative International Dictionary of English v.0.48:

Unambitious \Unambitious\
   See ambitious.

WordNet (r) 3.0 (2006):

unambitious
    adj 1: having little desire for success or achievement [syn:
           unambitious, ambitionless] [ant: ambitious]

Moby Thesaurus II by Grady Ward, 1.0:

22 Moby Thesaurus words for "unambitious":
   desireless, humble, inappetent, loveless, meek, modest, nirvanic,
   passionless, unaspiring, unassuming, unattracted, unboastful,
   undesirous, uneager, unenthusiastic, unimposing, unobtrusive,
   unostentatious, unpresuming, unpresumptuous, unpretending,
   unpretentious