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):

totter
    v 1: move without being stable, as if threatening to fall; "The
         drunk man tottered over to our table"
    2: walk unsteadily; "small children toddle" [syn: toddle,
       coggle, totter, dodder, paddle, waddle]
    3: move unsteadily, with a rocking motion [syn: teeter,
       seesaw, totter]

Moby Thesaurus II by Grady Ward, 1.0:

199 Moby Thesaurus words for "totter":
   age, alternate, amble, back and fill, barge, blunder, bowl along,
   break down, bundle, capsize, careen, career, cave in, change,
   cheat the undertaker, claudicate, clump, collapse, come a cropper,
   cower, crawl, creep, decline, dither, dodder, dogtrot, drag,
   drag along, drag out, droop, ebb and flow, equivocate, fade, fail,
   fall, fall down, fall flat, fall headlong, fall in, fall over,
   fall prostrate, falter, flounce, flounder, fluctuate, foot,
   footslog, founder, gait, gallop, get a cropper, get along, get on,
   go dead slow, go slow, go through phases, grow old, halt,
   hippety-hop, hitch, hobble, hop, idle, inch, inch along, jog,
   jog-trot, jolt, jump, labor, laze, limp, list, lock step, lumber,
   lunge, lurch, mince, mincing steps, mosey, oscillate, pace, paddle,
   peg, pendulate, piaffe, piaffer, pitch, pitch and plunge, plod,
   plunge, poke, poke along, prance, quake, quiver, rack, reel,
   ring the changes, rock, roll, sashay, saunter, scuff, scuffle,
   scuttle, seesaw, seethe, shake, shamble, shift, shilly-shally,
   shimmy, shiver, shrivel, shuffle, shuffle along, sidle,
   single-foot, sink, skip, slink, slither, slog, slouch, slowness,
   sprawl, spread-eagle, stagger, stagger along, stalk, stammer,
   stamp, step, stomp, straddle, straggle, stride, stroll,
   strolling gait, struggle, strut, stumble, stump, swagger, sway,
   swing, take a fall, take a flop, take a header, take a pratfall,
   take a spill, teeter, teeter-totter, tergiversate, thrash about,
   tilt, tittup, toddle, toddle along, topple, topple over, toss,
   toss and tumble, toss and turn, totter along, traipse, tread,
   tremble, trip, trot, trudge, tumble, turn, turn gray, turn turtle,
   turn white, vacillate, vary, velocity, volutation, waddle, walk,
   wallop, wallow, wamble, wane, waste away, waver, wax and wane,
   welter, wheel, wiggle, wither, wizen, wobble, worm, worm along,
   wrinkle