Oracle 11g Release 2

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with movie( genre, budget, title ) as
(
 select 'Western',1200000,'The Good, the Bad and the Ugly' from dual union all
 select 'Horror',806947,'Psycho' from dual union all
 select 'Crime',7000000,'The Godfather: Part III' from dual union all
 select 'Action',185000000,'The Dark Knight' from dual union all
 select 'Drama',26000000,'Philadelphia' from dual union all
 select 'Drama',13000000,'In the Name of the Father' from dual union all
 select 'Action',150000000,'Batman Begins' from dual union all
 select 'Historical',23800000,'The Last Emperor' from dual union all
 select 'Science-fiction',5800000,'Planet of the Apes' from dual union all
 select 'Crime',7000000,'The Godfather' from dual union all
 select 'Action',230000000,'The Dark Knight Rises' from dual union all
 select 'Comedy',28000000,'Zoolander' from dual union all
 select 'Crime',9000000,'Pulp Fiction' from dual union all
 select 'Crime',13000000,'The Godfather: Part II' from dual union all
 select 'War',70000000,'Saving Private Ryan' from dual union all
 select 'Science-fiction',28000000,'Blader Runner' from dual union all
 select 'Drama',33000000,'Gran Torino' from dual   
)
select genre, budget,title
  from
  (
      select genre, budget, title,
             row_number() over (partition by genre order by budget desc) as rn       
        from movie 
   )
  where rn = 1

GENRE	BUDGET	TITLE
Action	230000000	The Dark Knight Rises
Comedy	28000000	Zoolander
Crime	13000000	The Godfather: Part II
Drama	33000000	Gran Torino
Historical	23800000	The Last Emperor
Horror	806947	Psycho
Science-fiction	28000000	Blader Runner
War	70000000	Saving Private Ryan
Western	1200000	The Good, the Bad and the Ugly