The Collaborative International Dictionary of English v.0.48:

Naturally \Nat"u*ral*ly\, adv.
   In a natural manner or way; according to the usual course of
   things; spontaneously.
   [1913 Webster]

WordNet (r) 3.0 (2006):

naturally
    adv 1: as might be expected; "naturally, the lawyer sent us a
           huge bill" [syn: naturally, of course, course]
           [ant: unnaturally]
    2: according to nature; by natural means; without artificial
       help; "naturally grown flowers" [ant: artificially, by
       artificial means, unnaturally]
    3: through inherent nature; "he was naturally lazy" [syn:
       naturally, by nature]
    4: in a natural or normal manner; "speak naturally and easily"
       [ant: unnaturally]

Moby Thesaurus II by Grady Ward, 1.0:

138 Moby Thesaurus words for "naturally":
   OK, Roger, absolutely, accordingly, actually, all right, alright,
   alrighty, amen, and so, artlessly, as a consequence, as a result,
   as a rule, as expected, as per usual, as things go, as usual,
   as you say, assuredly, authentically, aye, by all means, by birth,
   by nature, candidly, casually, certainly, chiefly, clearly,
   commonly, congenitally, consequently, customarily, da, directly,
   easily, en famille, exactly, familiarly, finally, fine, generally,
   genetically, genuinely, good, good enough, guilelessly, habitually,
   hear, honestly, immanently, in plain English, in plain words,
   inconsequence, indeed, indeedy, inevitably, informally,
   ingenuously, innately, instinctively, internally, intrinsically,
   inwardly, it follows that, ja, just so, legitimately, logically,
   mainly, mais oui, matter-of-factly, most assuredly, most often,
   mostly, naturellement, necessarily, normally, normatively,
   obviously, of course, of necessity, offhand, offhandedly, okay,
   openheartedly, openly, ordinarily, originally, oui, plainly,
   point-blank, positively, precisely, prescriptively, primally,
   primitively, quite, rather, really, regularly, relaxedly, right,
   righto, sans ceremonie, simply, straightforwardly, sure,
   sure thing, surely, therefore, to be expected, to be sure,
   to the point, truly, unaffectedly, unassumedly, unassumingly,
   unceremoniously, unconstrainedly, unofficially, unpretentiously,
   usually, veridically, very well, warts and all, well and good,
   why yes, without ceremony, yea, yeah, yep, yes, yes indeed,
   yes indeedy, yes sir, yes sirree