The Collaborative International Dictionary of English v.0.48:

normally \nor"mal*ly\, adv.
   In a normal manner. --Darwin.
   [1913 Webster]

WordNet (r) 3.0 (2006):

normally
    adv 1: under normal conditions; "usually she was late" [syn:
           normally, usually, unremarkably, commonly,
           ordinarily] [ant: outstandingly, remarkably,
           unco, unusually]

Moby Thesaurus II by Grady Ward, 1.0:

43 Moby Thesaurus words for "normally":
   accustomedly, all in all, all things considered, altogether,
   as a rule, as a whole, as an approximation, as is usual,
   as per usual, as things go, as usual, at large, broadly,
   broadly speaking, by and large, chiefly, commonly, conventionally,
   customarily, generally, generally speaking, habitually, in general,
   mainly, most often, mostly, naturally, normatively, on balance,
   on the whole, ordinarily, overall, predominantly, prescriptively,
   prevailingly, regularly, roughly, roughly speaking, routinely,
   speaking generally, to be expected, usually, wontedly