The Collaborative International Dictionary of English v.0.48:

Quagmire \Quag"mire`\, n. [Quake + mire.]
   Soft, wet, miry land, which shakes or yields under the feet.
   "A spot surrounded by quagmires, which rendered it difficult
   of access." --Palfrey.
   [1913 Webster]

   Syn: Morass; marsh; bog; swamp; fen; slough.
        [1913 Webster] Quahog

WordNet (r) 3.0 (2006):

quagmire
    n 1: a soft wet area of low-lying land that sinks underfoot
         [syn: mire, quagmire, quag, morass, slack]

Moby Thesaurus II by Grady Ward, 1.0:

89 Moby Thesaurus words for "quagmire":
   baygall, bind, bog, bottom, bottomland, bottoms, box,
   buffalo wallow, cesspool, cloaca, cloaca maxima, clutch,
   complication, corner, crunch, dilemma, drain, dump,
   embarrassing position, embarrassment, everglade, fen, fenland,
   fine how-do-you-do, fix, garbage dump, glade, hell to pay, hobble,
   hog wallow, hole, holm, hot water, how-do-you-do, imbroglio, jam,
   marais, marish, marsh, marshland, meadow, mere, mess, mire, mix,
   moor, moorland, morass, moss, mud, mud flat, parlous straits, pass,
   peat bog, pickle, pinch, plight, predicament, pretty pass,
   pretty pickle, pretty predicament, quag, quicksand, salt marsh,
   scrape, septic tank, sewer, sink, slob land, slough, sough, spot,
   squeeze, stew, sticky wicket, strait, straits, sump, swale, swamp,
   swampland, taiga, tight spot, tight squeeze, tightrope,
   tricky spot, unholy mess, wallow, wash