The Collaborative International Dictionary of English v.0.48:

Brink \Brink\ (br[i^][ng]k), n. [Dan. brink edge, verge; akin to
   Sw. brink declivity, hill, Icel. brekka; cf. LG. brink a
   grassy hill, W. bryn hill, bryncyn hillock.]
   The edge, margin, or border of a steep place, as of a
   precipice; a bank or edge, as of a river or pit; a verge; a
   border; as, the brink of a chasm. Also Fig. "The brink of
   vice." --Bp. Porteus. "The brink of ruin." --Burke.
   [1913 Webster]

         The plashy brink of weedy lake.          --Bryant.
   [1913 Webster] brinkmanship

WordNet (r) 3.0 (2006):

brink
    n 1: a region marking a boundary [syn: brink, threshold,
         verge]
    2: the edge of a steep place
    3: the limit beyond which something happens or changes; "on the
       verge of tears"; "on the brink of bankruptcy" [syn: verge,
       brink]

Moby Thesaurus II by Grady Ward, 1.0:

35 Moby Thesaurus words for "brink":
   bank, board, border, bordure, brim, brow, coast, edge, featheredge,
   flange, frame, fringe, hem, labellum, labium, labrum, ledge, limb,
   limbus, lip, list, marge, margin, perimeter, periphery, point,
   ragged edge, rim, selvage, shore, side, sideline, skirt, threshold,
   verge