The Collaborative International Dictionary of English v.0.48:

Limerick \Lim"er*ick\ (l[i^]m"[~e]r*[i^]k), n. [Said to be from
   a song with the same verse construction, current in Ireland,
   the refrain of which contains the place name Limerick.]
   A humorous, often nonsensical, and sometimes risq['e] poem of
   five anapestic lines, of which lines 1, 2, and 5 are of three
   feet, and rhyme, and lines 3 and 4 are of two feet, and
   rhyme.

   Note: It often begins with "There once was a . . ." or "There
         was a . . ."; as

               There was a young lady, Amanda,
               Whose Ballades Lyriques were quite fin de
               Si[`e]cle, I deem
               But her Journal Intime
               Was what sent her papa to Uganda.
         [Webster 1913 Suppl. +PJC]

WordNet (r) 3.0 (2006):

Limerick
    n 1: port city in southwestern Ireland
    2: a humorous verse form of 5 anapestic lines with a rhyme
       scheme aabba

Moby Thesaurus II by Grady Ward, 1.0:

67 Moby Thesaurus words for "limerick":
   English sonnet, Horatian ode, Italian sonnet, Petrarchan sonnet,
   Pindaric ode, Sapphic ode, Shakespearean sonnet, alba, anacreontic,
   balada, ballad, ballade, bucolic, canso, chanson, clerihew, dirge,
   dithyramb, eclogue, elegy, epic, epigram, epithalamium, epode,
   epopee, epopoeia, epos, georgic, ghazel, haiku, idyll, jingle,
   lyric, madrigal, monody, narrative poem, nursery rhyme, ode,
   palinode, pastoral, pastoral elegy, pastorela, pastourelle, poem,
   prothalamium, rhyme, rondeau, rondel, roundel, roundelay, satire,
   sestina, sloka, song, sonnet, sonnet sequence, tanka, tenso,
   tenzone, threnody, triolet, troubadour poem, verse, verselet,
   versicle, villanelle, virelay