Here is a solution without a calendar table (which is a must in production). You might have date range in variables, or you might go for min() and max() from the_table.

EDIT: shorter version incorporating categories into date range generation

declare @startdate datetime = '2012-1-1'
declare @enddate datetime = '2012-1-5'

; with dates([date], category) as (
  select distinct @startdate, category
    from the_table
   union all
  select dateadd (day, 1, [date]), category
    from dates
   where [date] < @enddate
)
select dates.date, 
       dates.category, 
       isnull(the_table.amount, 0) Amount
  from dates
  left join the_table
    on dates.date = the_table.date
   and dates.category = the_table.category
 order by dates.category, dates.date
option (maxrecursion 0)

There is live test @ Sql Fiddle. New Sql Fiddle.