How to find the privileges and roles granted to a user in Oracle?

Look at http://docs.oracle.com/cd/B10501_01/server.920/a96521/privs.htm#15665

Check USER_SYS_PRIVS, USER_TAB_PRIVS, USER_ROLE_PRIVS tables with these select statements

SELECT * FROM USER_SYS_PRIVS; 
SELECT * FROM USER_TAB_PRIVS; 
SELECT * FROM USER_ROLE_PRIVS;

In addition to VAV's answer, The first one was most useful in my environment

select * from USER_ROLE_PRIVS where USERNAME='SAMPLE';
select * from USER_TAB_PRIVS where Grantee = 'SAMPLE';
select * from USER_SYS_PRIVS where USERNAME = 'SAMPLE';

Combining the earlier suggestions to determine your personal permissions (ie 'USER' permissions), then use this:

-- your permissions
select * from USER_ROLE_PRIVS where USERNAME= USER;
select * from USER_TAB_PRIVS where Grantee = USER;
select * from USER_SYS_PRIVS where USERNAME = USER;

-- granted role permissions
select * from ROLE_ROLE_PRIVS where ROLE IN (select granted_role from USER_ROLE_PRIVS where USERNAME= USER);
select * from ROLE_TAB_PRIVS  where ROLE IN (select granted_role from USER_ROLE_PRIVS where USERNAME= USER);
select * from ROLE_SYS_PRIVS  where ROLE IN (select granted_role from USER_ROLE_PRIVS where USERNAME= USER);

None of the other answers worked for me so I wrote my own solution:

As of Oracle 11g.

Replace USER with the desired username

Granted Roles:

SELECT * 
  FROM DBA_ROLE_PRIVS 
 WHERE GRANTEE = 'USER';

Privileges Granted Directly To User:

SELECT * 
  FROM DBA_TAB_PRIVS 
 WHERE GRANTEE = 'USER';

Privileges Granted to Role Granted to User:

SELECT * 
  FROM DBA_TAB_PRIVS  
 WHERE GRANTEE IN (SELECT granted_role 
                     FROM DBA_ROLE_PRIVS 
                    WHERE GRANTEE = 'USER');

Granted System Privileges:

SELECT * 
  FROM DBA_SYS_PRIVS 
 WHERE GRANTEE = 'USER';

If you want to lookup for the user you are currently connected as, you can replace DBA in the table name with USER and remove the WHERE clause.