Short Version - No, you really should just let it create the unique index and let it do it's job. Space is cheap. 

Edit - If you make the column you want unique the clustered index key, then you won't cost you any additional disk space, but it may slow down access to the table if your queries don't go through the unique column.

Long Version - Yes... but it burns CPU, increases disk I/O and slows down just about everything. 

You put an AFTER trigger on the table and have it count the number of records in the base table for the column you want to make unique. If the count is greater than 0 then rollback the transaction. 

**Example: (Of how NOT to do it)** 

 CREATE TABLE dbo.Test
 	(
 	TestID INT NOT NULL PRIMARY KEY IDENTITY(1,1)
 	, TestValue VARCHAR(100) NOT NULL
 	);
 
 GO
 
 CREATE TRIGGER trg_TestInsert ON dbo.Test AFTER INSERT, UPDATE
 AS
 BEGIN
 
 	DECLARE @DuplicateCount INT;
 	SET @DuplicateCount = 0;
 
 	;WITH CTE_Count AS
 		(
 		SELECT TestValue, COUNT(*) AS TestValueCount
 		FROM dbo.Test
 		GROUP BY TestValue
 		)
 	SELECT @DuplicateCount = COUNT(TestValue)
 	FROM CTE_Count
 	WHERE TestValueCount >=2;
 
 	IF @DuplicateCount >= 1
 	BEGIN
 		ROLLBACK;
 	END
 
 END;
 
 GO
 
 /** Test Insert Statement */
 INSERT INTO dbo.Test (TestValue)
 VALUES ('TestMe');
 
 INSERT INTO dbo.Test (TestValue)
 VALUES ('TestYou');
 
 --HINT: This one will fail.
 INSERT INTO dbo.Test (TestValue)
 VALUES ('TestYou');
 
 SELECT TestID, TestValue FROM dbo.Test;
 
 --Cleanup.
 DROP TABLE dbo.Test;