Square
There are infinitely many squares ending on 0, 1, 4, 5, 6, 9 and none ending on 2, 3, 7, 8.
Explanation
The first fifty squares are
0
1
4
9
16
25
36
49
64
81100
121
144
169
196
225
256
289
324
361400
441
484
529
576
625
676
729
784
841900
961
1024
1089
1156
1225
1296
1369
1444
15211600
1681
1764
1849
1936
2025
2116
2209
2304
2401
You can easily add more columns. The last digit follows the pattern 0, 1, 4, 9, 6, 5, 6, 9, 4, 1.