ExchangeRates.Date <= Documtnt.Date 

ДОБАВИЛ Document.Date>=ExchangeRates.Date

SELECT * 
FROM DocumentSum 
INNER JOIN DocumentBody ON DocumentSum.IdDocumentBody = DocumentBody.Id 
INNER JOIN Document ON DocumentBody.IdDocument = Document.Id 
LEFT OUTER JOIN DocumentFixedAssets ON DocumentBody.Id = DocumentFixedAssets.IdDocumentBody 
INNER JOIN ExchangeRates ON Document.IdCurrency=ExchangeRates.IdDirectory2 
WHERE (DocumentFixedAssets.IdDocumentBody IS NULL) 
AND (ExchangeRates.IdDirectory1=@VIdCurrencyM2) AND (Document.Date>=ExchangeRates.Date); 

CROSS APPLY (
SLECT TOP 1 <Rate>
FROM Currency  x
WHERE 
 <x.IdCurr> = <IdCurr> AND
 <x.Date> <= <Date>
ORDER BY Date DESC
) as x

declare @doc table (id int, dt date, id_cur int)
declare @cur table (id int, dt date, cur decimal(10,4))

insert @cur
values(1,'2016-01-01', 10),(1,'2016-01-09', 11),(1,'2016-01-20', 20)

insert @doc
values(1,'2016-01-10',1),(2,'2016-01-21',1)


select
*
from
@doc dc
cross apply(select top 1 cur from @cur cr where cr.id=dc.id_cur and cr.dt<=dc.dt order by cr.dt desc)c

select
*, (select top 1 cur from @cur cr where cr.id=dc.id_cur and cr.dt<=dc.dt order by cr.dt desc) as cur
from
@doc dc