In SQL how do I get the maximum value for an integer?

In Mysql there is a cheap trick to do this:

mysql> select ~0;
+----------------------+
| ~0                   |
+----------------------+
| 18446744073709551615 |
+----------------------+

the tilde is the bitwise negation. The resulting value is a bigint. See: http://dev.mysql.com/doc/refman/5.1/en/bit-functions.html#operator_bitwise-invert

For the other integer flavours, you can use the right bitshift operator >> like so:

SELECT ~0 as max_bigint_unsigned
,      ~0 >> 32 as max_int_unsigned
,      ~0 >> 40 as max_mediumint_unsigned
,      ~0 >> 48 as max_smallint_unsigned
,      ~0 >> 56 as max_tinyint_unsigned
,      ~0 >> 1  as max_bigint_signed
,      ~0 >> 33 as max_int_signed
,      ~0 >> 41 as max_mediumint_signed
,      ~0 >> 49 as max_smallint_signed
,      ~0 >> 57 as max_tinyint_signed
\G

*************************** 1. row ***************************
   max_bigint_unsigned: 18446744073709551615
      max_int_unsigned: 4294967295
max_mediumint_unsigned: 16777215
 max_smallint_unsigned: 65535
  max_tinyint_unsigned: 255
     max_bigint_signed: 9223372036854775807
        max_int_signed: 2147483647
  max_mediumint_signed: 8388607
   max_smallint_signed: 32767
    max_tinyint_signed: 127
1 row in set (0.00 sec)