--Table
BEGIN
   EXECUTE IMMEDIATE 'DROP TABLE mytable';
EXCEPTION
   WHEN OTHERS THEN
      IF SQLCODE != -942 THEN
         RAISE;
      END IF;
END;

ADDENDUM For reference, here are the equivalent blocks for other object types:

--Sequence

BEGIN
  EXECUTE IMMEDIATE 'DROP SEQUENCE sequence_name';
EXCEPTION
  WHEN OTHERS THEN
    IF SQLCODE != -2289 THEN
      RAISE;
    END IF;
END;

--View

BEGIN
  EXECUTE IMMEDIATE 'DROP VIEW view_name';
EXCEPTION
  WHEN OTHERS THEN
    IF SQLCODE != -942 THEN
      RAISE;
    END IF;
END;

--Trigger

BEGIN
  EXECUTE IMMEDIATE 'DROP TRIGGER ' || trigger_name;
EXCEPTION
  WHEN OTHERS THEN
    IF SQLCODE != -4080 THEN
      RAISE;
    END IF;
END;

--Index

BEGIN
  EXECUTE IMMEDIATE 'DROP INDEX index_name';
EXCEPTION
  WHEN OTHERS THEN
    IF SQLCODE != -1418 THEN
      RAISE;
    END IF;
END;

--Column

BEGIN
  EXECUTE IMMEDIATE 'ALTER TABLE ' || table_name
                || ' DROP COLUMN ' || column_name;
EXCEPTION
  WHEN OTHERS THEN
    IF SQLCODE != -904 THEN
      RAISE;
    END IF;
END;

--Database Link

BEGIN
  EXECUTE IMMEDIATE 'DROP DATABASE LINK  dblink_name';
EXCEPTION
  WHEN OTHERS THEN
    IF SQLCODE != -2024 THEN
      RAISE;
    END IF;
END;

--Materialized View

BEGIN
  EXECUTE IMMEDIATE 'DROP MATERIALIZED VIEW mview_name';
EXCEPTION
  WHEN OTHERS THEN
    IF SQLCODE != -12003 THEN
      RAISE;
    END IF;
END;

--Type

BEGIN
  EXECUTE IMMEDIATE 'DROP TYPE type_name';
EXCEPTION
  WHEN OTHERS THEN
    IF SQLCODE != -4043 THEN
      RAISE;
    END IF;
END;

--Constraint

BEGIN
  EXECUTE IMMEDIATE 'ALTER TABLE ' || table_name
            || ' DROP CONSTRAINT ' || constraint_name;
EXCEPTION
  WHEN OTHERS THEN
    IF SQLCODE != -2443 THEN
      RAISE;
    END IF;
END;

--Scheduler Job

BEGIN
  DBMS_SCHEDULER.drop_job(job_name);
EXCEPTION
  WHEN OTHERS THEN
    IF SQLCODE != -27475 THEN
      RAISE;
    END IF;
END;

--User / Schema

BEGIN
  EXECUTE IMMEDIATE 'DROP USER ' || user_name;
  /* you may or may not want to add CASCADE */
EXCEPTION
  WHEN OTHERS THEN
    IF SQLCODE != -1918 THEN
      RAISE;
    END IF;
END;

--Package

BEGIN
  EXECUTE IMMEDIATE 'DROP PACKAGE ' || package_name;
EXCEPTION
  WHEN OTHERS THEN
    IF SQLCODE != -4043 THEN
      RAISE;
    END IF;
END;

--Procedure

BEGIN
  EXECUTE IMMEDIATE 'DROP PROCEDURE ' || procedure_name;
EXCEPTION
  WHEN OTHERS THEN
    IF SQLCODE != -4043 THEN
      RAISE;
    END IF;
END;

--Function

BEGIN
  EXECUTE IMMEDIATE 'DROP FUNCTION ' || function_name;
EXCEPTION
  WHEN OTHERS THEN
    IF SQLCODE != -4043 THEN
      RAISE;
    END IF;
END;

--Tablespace

BEGIN
  EXECUTE IMMEDIATE 'DROP TABLESPACE' || tablespace_name;
EXCEPTION
  WHEN OTHERS THEN
    IF SQLCODE != -959 THEN
      RAISE;
    END IF;
END;