GRANT privileges to table elements
Sequences are separate objects with separate privileges.


  Granting permission on a table does not automatically extend
  permissions to any sequences used by the table, including sequences
  tied to SERIAL columns. Permissions on sequences must be set
  separately.


Indexes belong to the table. To DROP or CREATE an index you must be the owner of the table (or superuser).

Columns go with table privileges. Granting privileges on the table grants applicable privileges to all columns automatically.

For DDL commands (ALTER TABLE ...) you must own the table again.

Since PostgreSQL 9.1 there are column level DML-grants additionally. But:


  A user may perform SELECT, INSERT, etc. on a column if he holds that
  privilege for either the specific column or its whole table. Granting
  the privilege at the table level and then revoking it for one column
  will not do what you might wish: the table-level grant is unaffected
  by a column-level operation.


More details in the manual about GRANT, where the quotes are from.