In which cases will Oracle create indexes automatically?

I'll try to consolidate given answers and make it community wiki.
So indexes are automatically created by Oracle for such cases:

1. APC: For primary key and unique key unless such indexes already exist.
2. APC: For LOB storage and XMLType.
3. Gary: For table with a nested table.
4. Jim Hudson: For materialized view.

Firstly, Oracle does not always create an index when we create a primary or unique key. If there is already an index on that column it will use it instead...

SQL> create table t23 (id number not null)  2  /Table created.SQL> create index my_manual_idx on t23 ( id )  2  /Index created.SQL> select index_name from user_indexes  2  where table_name = 'T23'  3  /INDEX_NAME------------------------------MY_MANUAL_IDXSQL> 

... note that MY_MANUAL_IDX is not a unique index; it doesn't matter ...

SQL> alter table t23  2      add constraint t23_pk primary key (id) using index  3  /Table altered.SQL> select index_name from user_indexes  2  where table_name = 'T23'  3  /INDEX_NAME------------------------------MY_MANUAL_IDXSQL> drop index my_manual_idx  2  /drop index my_manual_idx           *ERROR at line 1:ORA-02429: cannot drop index used for enforcement of unique/primary keySQL> 

There is another case when Oracle will automatically create an index: LOB storage....

SQL> alter table t23  2      add txt clob  3      lob (txt) store as basicfile t23_txt (tablespace users)  4  /Table altered.SQL> select index_name from user_indexes  2  where table_name = 'T23'  3  /INDEX_NAME------------------------------MY_MANUAL_IDXSYS_IL0000556081C00002$$SQL>

edit

The database treats XMLType same as other LOBs...

SQL> alter table t23  2      add xmldoc xmltype  3  /Table altered.SQL> select index_name from user_indexes  2  where table_name = 'T23'  3  /INDEX_NAME------------------------------MY_MANUAL_IDXSYS_IL0000556081C00002$$SYS_IL0000556081C00004$$SQL>    

No, we're getting closer but that's not quite a complete list yet.

There will also be an index automatically created when you create materialized view since Oracle needs to be able to quickly identify the rows when doing a fast refresh. For rowid based materialized views, it uses I_SNAP$_tablename. For primary key materialized views, it uses the original PK name, modified as necessary to make it unique.

create materialized view testmv refresh force with rowidas select * from dual;select index_name from user_indexes where table_name = 'TESTMV';Index Name--------------I_SNAP$_TESTMV