The Collaborative International Dictionary of English v.0.48:

Thickness \Thick"ness\, n. [AS. ?icnes.]
   The quality or state of being thick (in any of the senses of
   the adjective).
   [1913 Webster]

WordNet (r) 3.0 (2006):

thickness
    n 1: the dimension through an object as opposed to its length or
         width [ant: slenderness, tenuity, thinness]
    2: indistinct articulation; "judging from the thickness of his
       speech he had been drinking heavily"
    3: used of a line or mark [syn: thickness, heaviness]
    4: resistance to flow [ant: thinness]

Moby Thesaurus II by Grady Ward, 1.0:

121 Moby Thesaurus words for "thickness":
   adhesiveness, band, bed, bedding, belt, bodily size, body, bulk,
   cacophony, clabbering, clamminess, closeness, clotting,
   coagulation, coarseness, colloidality, compactness, congestedness,
   congestion, consistence, consistency, corpulence, couche, course,
   cracked voice, crowdedness, curdling, deck, denseness, density,
   depth, discord, distance through, doughiness, dryness, fatness,
   firmness, floor, gallery, gelatinity, gelatinousness, gluelikeness,
   gluiness, glutinosity, glutinousness, grossness, gruffness,
   gumlikeness, gumminess, gutturalism, gutturality, gutturalness,
   hardness, harshness, heaviness, hoarseness, huskiness,
   impenetrability, impermeability, imporosity, incompressibility,
   incrassation, inspissation, jammedness, jellification,
   jellylikeness, layer, ledge, lentor, level, mass, measures,
   mucilaginousness, overlayer, overstory, pastiness, raspiness,
   raucity, relative density, ropiness, roughness, rudeness,
   scrapiness, scratchiness, seam, shelf, slabbiness, sliminess,
   solidity, solidness, specific gravity, spissitude, stage, step,
   stertorousness, stickiness, stodginess, story, stratum,
   stringiness, substratum, superstratum, syrupiness, tackiness,
   tenaciousness, tenacity, the third dimension, thickening,
   throatiness, tier, topsoil, toughness, treacliness, ugliness,
   underlayer, understory, understratum, viscidity, viscosity,
   viscousness, zone