Grant all to a user doesn't grant create index privilege

To be able to create and index you must have the create index system privilege.  You can assign this using:

grant create index to my_user

Why do you want a user creating their own index on a table they don't own?

Does the user have the privs to create objects in the database?

Are they trying to create a local index in their schema or in your schema?

Sorry, I'm talking rubbish, I'm thinking of the create any index system privilege.  As you correct say GRANT INDEX.... should be enough.

What error are you getting?

If you are connected to my_user and my_user owns the table my_table then there is no point issuing the following grant:

grant all on my_table to my_user

Providing you have the CREATE TABLE system privilege you should be able to create tables in your own schema and query, insert, update, delete and create indexes on those tables as you own them.

You only need to grant these privileges on your tables to "other" users.

grant all on me.my_table to other_user.  other_usercan create a table , but cannot create an index.  The following is the error.

ERROR at line 1:
ORA-01031: insufficient privileges

You have prefixed my_table with a schema name which suggests that the current Oracle schema from which you are running the statement doesn't own my_table.

You can only grant privileges to tables that you own or for which you have been given the GRANT OPTION e.g.

connect user_a

create table x.....;

grant all on x to user_b WITH GRANT OPTION;

connect user_b

grant all on user_a.x to user_c;

Again:  Are they trying to create a local index in their schema or in your schema?

They should be able to do:
create index my_index on me.my_table;

Unless you want to give them permission to create an object in your schema they won't be able to do:
create index me.my_index on me.my_table;

I am still curious why you want them creating indexes on your tables.

I want them to create table on my schema, and also create a index on my schema.  Strange thing is they can create a table, not a index.  

grant all on a table to a user doesn't grant the create index to the user. grant any index will do.

Remember, granting 'ANY' means any.  They can create indexes in the SYS schema.

Just to clarify, the GRANT ANY INDEX is very powerful and as slightwv says it will allow users to create indexes in any schema.

Providing a user has been granted index privilege on a table they should be able to create an index on that table e.g.

connect john;

create table accounts ......;

grant index on accounts to fred;

connect fred;

create index freds_index on john.accounts;