The Collaborative International Dictionary of English v.0.48:

Mesquite \Mes*qui"te\ (m[e^]s*k[=e]"t[asl]), Mesquit \Mes*quit"\
   (m[e^]s*k[=e]t"), n. [Sp. mezquite; said to be a Mexican
   Indian word.] (Bot.)
   Aany of several small spiny trees or shrubs of the
   southwestern part of North America belonging to the genus
   Prosopis having small flowers in axillary cylindrical
   spikes followed by large sugar-rich pods, especially the
   honey mesquite, and screw-pod mesquite.
   [1913 Webster + WordNet 1.5]

   Honey mesquite. See Algaroba
   (b) .

   Screw-pod mesquite, a smaller tree (Prosopis pubescens),
      having spiral pods used as fodder and sometimes as food by
      the Indians.

   Mesquite grass, a rich native grass in Western Texas
      (Bouteloua oligostachya, and other species); -- so
      called from its growing in company with the mesquite tree;
      -- called also muskit grass, grama grass.
      [1913 Webster]

WordNet (r) 3.0 (2006):

mesquite
    n 1: any of several small spiny trees or shrubs of the genus
         Prosopis having small flowers in axillary cylindrical
         spikes followed by large pods rich in sugar [syn:
         mesquite, mesquit]

U.S. Gazetteer Places (2000):

Mesquite, NV -- U.S. city in Nevada
   Population (2000):    9389
   Housing Units (2000): 4442
   Land area (2000):     15.309435 sq. miles (39.651253 sq. km)
   Water area (2000):    0.335395 sq. miles (0.868670 sq. km)
   Total area (2000):    15.644830 sq. miles (40.519923 sq. km)
   FIPS code:            46000
   Located within:       Nevada (NV), FIPS 32
   Location:             36.802582 N, 114.082168 W
   ZIP Codes (1990):
   Note: some ZIP codes may be omitted esp. for suburbs.
   Headwords:
    Mesquite, NV
    Mesquite


U.S. Gazetteer Places (2000):

Mesquite, NM -- U.S. Census Designated Place in New Mexico
   Population (2000):    948
   Housing Units (2000): 276
   Land area (2000):     0.825660 sq. miles (2.138450 sq. km)
   Water area (2000):    0.000000 sq. miles (0.000000 sq. km)
   Total area (2000):    0.825660 sq. miles (2.138450 sq. km)
   FIPS code:            48270
   Located within:       New Mexico (NM), FIPS 35
   Location:             32.162976 N, 106.693434 W
   ZIP Codes (1990):     88048
   Note: some ZIP codes may be omitted esp. for suburbs.
   Headwords:
    Mesquite, NM
    Mesquite


U.S. Gazetteer Places (2000):

Mesquite, TX -- U.S. city in Texas
   Population (2000):    124523
   Housing Units (2000): 46245
   Land area (2000):     43.415940 sq. miles (112.446764 sq. km)
   Water area (2000):    0.048415 sq. miles (0.125395 sq. km)
   Total area (2000):    43.464355 sq. miles (112.572159 sq. km)
   FIPS code:            47892
   Located within:       Texas (TX), FIPS 48
   Location:             32.782878 N, 96.609862 W
   ZIP Codes (1990):     75149 75150 75181 75182
   Note: some ZIP codes may be omitted esp. for suburbs.
   Headwords:
    Mesquite, TX
    Mesquite