The Collaborative International Dictionary of English v.0.48:

Totter \Tot"ter\, v. i. [imp. & p. p. Tottered; p. pr. & vb.
   n. Tottering.] [Probably for older tolter; cf. AS.
   tealtrian to totter, vacillate. Cf.Tilt to incline,
   Toddle, Tottle, Totty.]
   1. To shake so as to threaten a fall; to vacillate; to be
      unsteady; to stagger; as, an old man totters with age. "As
      a bowing wall shall ye be, and as a tottering fence."
      --Ps. lxii. 3.
      [1913 Webster]

   2. To shake; to reel; to lean; to waver.
      [1913 Webster]

            Troy nods from high, and totters to her fall.
                                                  --Dryden.
      [1913 Webster]

WordNet (r) 3.0 (2006):

tottering
    adj 1: unsteady in gait as from infirmity or old age; "a
           tottering skeleton of a horse"; "a tottery old man" [syn:
           tottering, tottery]
    2: (of structures or institutions) having lost stability;
       failing or on the point of collapse; "a tottering empire"

Moby Thesaurus II by Grady Ward, 1.0:

176 Moby Thesaurus words for "tottering":
   Lissajous figure, alternation, ambling, ambulation, anile,
   back-and-forth, backpacking, cautious, circumspect, claudicant,
   collapsing, coming and going, crabbed, crawling, creeping,
   creeping like snail, debilitated, deciduous, declining,
   declivitous, decrepit, decurrent, deliberate, descendant,
   descending, dilapidated, doddered, doddering, doddery, down,
   down-reaching, downcoming, downfalling, downgoing, downhill,
   downsinking, downward, drooping, dropping, easy, ebb and flow,
   falling, faltering, feeble, flagging, fluctuation, flux and reflux,
   foot-dragging, footing, footing it, footwork, fossilized, gentle,
   gerontal, gerontic, going on foot, gradual, groggy, halting,
   hiking, hitchhiking, hitching, hobbled, hobbling, hoofing, idle,
   indolent, infirm, languid, languorous, lazy, legwork, leisurely,
   limping, lumbering, marching, moderate, mossbacked, moth-eaten,
   mummylike, on the decline, on the descendant, on the downgrade,
   on the skids, on the wane, oscillation, palsied, papery-skinned,
   pedestrianism, pendulation, perambulation, plummeting, plunging,
   poking, poky, ramshackle, ravaged with age, reciprocation, relaxed,
   reluctant, rhythmic play, ricketish, rickety, rocky, run to seed,
   rusty, sagging, sauntering, seesaw, seesawing, senile, setting,
   shaky, shifting, shriveled, shuffling, sine wave, sinking, slack,
   slothful, slow, slow as death, slow as molasses, slow as slow,
   slow-crawling, slow-foot, slow-going, slow-legged, slow-moving,
   slow-paced, slow-poky, slow-running, slow-sailing, slow-stepped,
   sluggish, snail-paced, snaillike, spidery, spindly, staggering,
   stricken in years, strolling, submerging, subsiding, teeter,
   teeter-totter, teeter-tottering, teetering, teetery, tentative,
   thumbing, thumbing a ride, timeworn, to-and-fro, toddling,
   tortoiselike, tottery, tramping, treading, trudging, tumbledown,
   turtlelike, unhurried, unsteady, ups and downs, vacillation,
   variation, vicissitude, waddling, walking, wavering, weak, wigwag,
   withered, wizened, wobbly