CREATE TABLE #tmp(Dt DATETIME NOT NULL PRIMARY KEY CLUSTERED);

INSERT INTO #tmp VALUES ('20130101'),('20130102'),('20130104'),('20130105'),('20130106'),('20130109');

SELECT 
	a.Dt AS [NextDate(s) Missing]
FROM
	#tmp a
	LEFT JOIN #tmp b ON
		a.Dt = b.Dt-1
WHERE
	b.Dt IS NULL 
	
DROP TABLE #tmp;

Raw Data

ID    |Row    |Start Date  |End Date
0052  |1      |10/01/2012  |12/31/2012        
0052  |2      |01/01/2013  |12/31/2013        
0054  |1      |10/01/2012  |12/31/2012        
0054  |2      |02/01/2013  |12/31/2013        

Result
ID    |Row    |Start Date  |End Date   
0052  |1      |01/01/2013  |12/31/2013   
0054  |1      |10/01/2012  |12/31/2012    
0054  |2      |02/01/2013  |12/31/2013   

ID    |Row    |Start Date  |End Date
0052  |1      |10/01/2012  |12/31/2012        
0052  |2      |01/01/2013  |12/31/2013  
0052  |3      |01/01/2014  |12/31/2014  
0054  |1      |10/01/2012  |12/31/2012        
0054  |2      |02/01/2013  |12/31/2013  

CREATE TABLE #tmp(ID INT, [Row] INT, [StartDate] DATETIME, endDate DATETIME);
INSERT INTO #tmp VALUES
(52,1,'10/1/2012','12/31/2012'),
(52,2,'1/1/2013','12/31/2013'),
(52,3,'1/1/2014','12/31/2014'),
(52,4,'1/2/2015','12/31/2015'),
(54,1,'10/1/2012','12/31/2012'),
(54,2,'2/1/2013','12/31/2013');

---ONE WAY

;WITH cte AS
(
	SELECT
		a.*,
		COALESCE(b.hasNext,0) hasNext,
		COALESCE(c.hasPrevious,0) AS hasPrevious
	FROM
		#tmp a
		OUTER APPLY
		( 
			SELECT CASE WHEN b.StartDate = DATEADD(dd,1,a.EndDate) THEN 1 ELSE 0 END AS hasNext
			FROM #tmp b WHERE b.id = a.id AND a.row+1 = b.row
		)b
		OUTER APPLY
		(
			SELECT CASE WHEN a.StartDate = DATEADD(dd,1,b.EndDate) THEN 1 ELSE 0 END AS hasPrevious
			FROM #tmp b WHERE b.id = a.id AND a.row = b.row+1
		) c
)
SELECT
	a.Id, a.Row, a.StartDate,
	COALESCE(b.EndDate,a.EndDate) EndDate
FROM
	cte a
	OUTER  APPLY
	(
		SELECT MIN(EndDate) EndDate FROM cte b
		WHERE b.id = a.id AND b.hasNext = 0 AND b.EndDate >= a.EndDate
	) b
WHERE
	a.hasPrevious = 0;


--- ANOTHER WAY
;WITH cte AS
(
	SELECT *,
		endDate AS newEndDate,
		ROW_NUMBER() OVER (PARTITION BY id ORDER BY id,row) AS RN,
		1 AS Lvl
	FROM #tmp a 
	WHERE NOT EXISTS ( SELECT * FROM #tmp b WHERE b.id = a.ID
	AND a.StartDate = DATEADD(dd,1,b.EndDate))
	
	UNION ALL
	
	SELECT t.*, t.EndDate AS NewEndDate, RN, lvl+1
	FROM #tmp t
	INNER JOIN cte c ON c.id = t.id AND c.row +1 = t.row 
		AND t.StartDate = DATEADD(dd,1,c.endDate)
),
cte2 AS 
(
SELECT id,row,startdate, lvl,
	MAX(newEndDate) OVER (PARTITION BY Id, RN) AS NewEndDate
FROM
	cte
)
SELECT id,row,startdate, newenddate FROM cte2 WHERE lvl = 1
ORDER BY id, row;

drop table #tmp;