Oracle Equivalent to MySQL INSERT IGNORE?

If you're on 11g you can use the hint IGNORE_ROW_ON_DUPKEY_INDEX:

SQL> create table my_table(a number, constraint my_table_pk primary key (a));

Table created.

SQL> insert /*+ ignore_row_on_dupkey_index(my_table, my_table_pk) */
  2  into my_table
  3  select 1 from dual
  4  union all
  5  select 1 from dual;

1 row created.