In Oracle 12.1 and below: 30 char (bytes, really, as has been stated).
But do not trust me; try this for yourself:
SQL> create table I23456789012345678901234567890 (my_id number);
Table created.
SQL> create table I234567890123456789012345678901(my_id number);
ERROR at line 1:
ORA-00972: identifier is too long
Updated: as stated above, in Oracle 12.2 and later, the maximum object name length is now 128 bytes.