You could use GatherBy:
(The pure function just presents the first part of each pair to GatherBy.)
In[2]:= pairs = RandomInteger[{1, 10}, {30, 2}]
Out[2]= {{8, 2}, {9, 6}, {7, 10}, {2, 4}, {9, 9}, {10, 2}, {8,
10}, {3, 1}, {10, 2}, {2, 4}, {8, 5}, {1, 1}, {2, 8}, {10, 9}, {10,
10}, {5, 7}, {4, 6}, {3, 6}, {1, 6}, {6, 10}, {2, 5}, {3, 4}, {8,
10}, {2, 10}, {10, 8}, {4, 8}, {1, 7}, {5, 4}, {6, 4}, {8, 10}}
In[3]:= GatherBy[pairs, #[[1]] &]
Out[3]= {{{8, 2}, {8, 10}, {8, 5}, {8, 10}, {8, 10}}, {{9, 6}, {9,
9}}, {{7, 10}}, {{2, 4}, {2, 4}, {2, 8}, {2, 5}, {2, 10}}, {{10,
2}, {10, 2}, {10, 9}, {10, 10}, {10, 8}}, {{3, 1}, {3, 6}, {3,
4}}, {{1, 1}, {1, 6}, {1, 7}}, {{5, 7}, {5, 4}}, {{4, 6}, {4,
8}}, {{6, 10}, {6, 4}}}
