you may look at DBA_TAB_PRIVS for grants on objects, on DBA_SYS_PRIVS for system privileges and on DBA_ROLE_PRIVS to see which roles are granted.
If you are not allowed to see the DBA_* views you may look at the series of views that start with USER_*: USER_TAB_PRIVS, USER_SYS_PRIVS and USER_ROLE_PRIVS.
These views will tell you only the privileges granted the schema you are connected with.
regards,
astropp