This is possible if you are using tsql (i.e. microsoft sql server. You also tagged your question with MySql which is another brand of database) with a sql server that supports ROW_NUMBER (i.e. Sql Server 2005 or later).
I'm assuming that ReqstDate, ConfDate and ShippedDate are nvarchars (otherwise it would be impossible to have the value '99/99/9999' in those fields). You should convert those columns into datetime fields otherwise all the ORDER BY clauses in the query will go wrong when you get a value like 01/15/2012 (The query works for the dataset you gave but only because the datetime values are all near each other in time so that the alphabetical order is equal to the chronological order). Off course, if you you are going to do this, you will need to use NULL for '99/99/9999' and in the query change '!= '99/99/9999'' to 'is null'.
However, I would advise to use a reporting tool or a simple select and some code to generate the table you want. The query is rather complex and difficult to maintain. As a general rule, a database provides the caller with data while all the formatting should be done by the caller itself.
Edit : Mikael Eriksson's answer is better & simpler than mine. My remark about the datetime fields still stands however.
select case when ROW_NUMBER() over (partition by [Order] Order by [order]) = 1
and [order] != 0
then cast([Order] as nvarchar)
else ''
end as [order],
case when ROW_NUMBER() over (partition by [order], num
Order by [order], num) = 1
and num != 0
then cast(num as nvarchar)
else ''
end as num,
case when ROW_NUMBER() over (partition by [order], num, Material
Order by [order], num, Material) = 1
then Material
else ''
end as Material,
case when ROW_NUMBER() over (partition by [order], num, Material, ReqstDate
Order by [order], num, Material, ReqstDate) = 1
and ReqstDate != '99/99/9999'
then ReqstDate
else ''
end as ReqstDate,
case when ROW_NUMBER() over (partition by [order], num, Material, ReqstDate, ReqstQty
Order by [order], num, Material, ReqstDate, ReqstQty) = 1
and ReqstQty != 0
then cast(ReqstQty as nvarchar)
else ''
end as ReqstQty,
case when ROW_NUMBER() over (partition by [order], num, Material, ReqstDate, ReqstQty, ConfDate
Order by [order], num, Material, ReqstDate, ReqstQty, ConfDate) = 1
and ConfDate != '99/99/9999'
then ConfDate
else ''
end as ConfDate,
case when ROW_NUMBER() over (partition by [order], num, Material, ReqstDate, ReqstQty, ConfDate, ConfQty
Order by [order], num, Material, ReqstDate, ReqstQty, ConfDate, ConfQty) = 1
and ConfQty != 0
then cast(ConfQty as nvarchar)
else ''
end as ConfQty,
case when ROW_NUMBER() over (partition by ShippedDate, num, Material, ReqstDate, ReqstQty, ConfDate, ConfQty, ShippedDate
Order by ShippedDate, num, Material, ReqstDate, ReqstQty, ConfDate, ConfQty, ShippedDate) = 1
and ShippedDate != '99/99/9999'
then ShippedDate
else ''
end as ShippedDate,
case when ROW_NUMBER() over (partition by [order], num, Material, ReqstDate, ReqstQty, ConfDate, ConfQty, ShippedDate, ShippedQty
Order by [order], num, Material, ReqstDate, ReqstQty, ConfDate, ConfQty, ShippedDate, ShippedQty) = 1
and ShippedQty != 0
then cast(ShippedQty as nvarchar)
else ''
end as ShippedQty
from yourTable
order by ROW_NUMBER() over (order by [order], num, Material, ReqstDate, ReqstQty, ConfDate, ConfQty, ShippedDate, ShippedQty)