Does this data only work with dates, and never times (such as what GETDATE() would return?). The reason I ask is that it basically skips a day worth of minutes between, say, 6/30/14 00:00:00.003 and 6/30/14 23:59:59.957.
However, if you're simply doing this for reporting purposes and not detection logic, the easiest way is to dual query the information (you have to do this), and find the minimum date for your key greater than the current row's value. This is most easily done with Outer Apply:
IF OBJECT_ID ('tempdb..#cattimelines') IS NOT NULL
DROP TABLE #cattimelines
Create table #cattimelines (categoryID int, EffectiveDate datetime, CategoryValue varchar(11))
INSERT INTO #cattimelines(categoryID, EffectiveDate, CategoryValue) VALUES(1000, '2014-01-01', 'A')
INSERT INTO #cattimelines(categoryID, EffectiveDate, CategoryValue) VALUES(1000, '2014-02-01', 'B')
INSERT INTO #cattimelines(categoryID, EffectiveDate, CategoryValue) VALUES(1000, '2014-04-01', 'C')
INSERT INTO #cattimelines(categoryID, EffectiveDate, CategoryValue) VALUES(1000, '2014-07-01', 'A')
SELECT
ct.CategoryID,
EffectiveDate AS StartDate,
DATEADD( dd, -1, drv.MinED) AS EndDate,
CategoryValue
FROM
#cattimelines AS ct
OUTER APPLY
(SELECT
ct2.CategoryID,
MIN( ct2.EffectiveDate) AS MinED
FROM
#cattimelines AS ct2
WHERE
ct.EffectiveDate < ct2.EffectiveDate
AND ct.CategoryID = ct2.CategoryID
GROUP BY
ct2.CategoryID
) AS drv
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