Performance hit using CAST in T-SQL
If the cast of the column is to exactly the same datatype and length and the seek predicate is a literal it does indeed seem to disregard it or treat it as a no-op and does an index seek on equality.

Seek Keys[1]: Prefix: [tempdb].[dbo].[#test].name = Scalar Operator(N'rpc')


If the cast of the column is to the same datatype but greater length and the seek predicate is a string literal it causes an index scan. This is obviously to be avoided.

If the cast of the column is to the same datatype and the same or greater length and the seek predicate is a local variable it adds a compute scalar operator to the execution plan. This  calls GetRangeThroughConvert and outputs a range.

This range is used to do an index seek and seems pretty efficient

Seek Keys[1]: 
Start: [tempdb].[dbo].[#test].name &gt; Scalar Operator([Expr1006]), 
End: [tempdb].[dbo].[#test].name &lt; Scalar Operator([Expr1007])


Testing Code

SELECT *
 INTO #test
  FROM [master].[dbo].[spt_values]

CREATE NONCLUSTERED INDEX [ixname] ON #test
(
    [name] ASC
)

DECLARE @name NVARCHAR(MAX)

SET @name = 'rpc'

SELECT name
FROM #test
WHERE CAST(name AS NVARCHAR(35))= @name --Cast the same and local variable

SELECT name
FROM #test
WHERE CAST(name AS NVARCHAR(MAX))=@name --Cast to longer and local variable

SELECT name
FROM #test
WHERE CAST(name AS NVARCHAR(35))='rpc' --Cast the same and literal

SELECT name
FROM #test
WHERE CAST(name AS NVARCHAR(MAX))='rpc' --Cast to longer and literal