Postgresql generate_series dynamic interval

I really do not see a point of using generate_series.

To get result that you proposed you could use ROW_NUMBER and self-join:

CREATE TABLE tab(cleaning timestamp);

INSERT INTO tab(cleaning)
VALUES ('2015-03-01 00:00'), ('2015-05-31 00:00'), ('2015-06-13 00:00');

Main query:

WITH cte AS
(
   SELECT cleaning, ROW_NUMBER() OVER(ORDER BY cleaning) AS rn
   FROM tab
)
SELECT COALESCE(c1.cleaning,'0001-01-01'::timestamp) AS start_date,
       COALESCE(c2.cleaning,CURRENT_TIMESTAMP) AS end_date
FROM cte c1
FULL JOIN cte c2
  ON c1.rn = c2.rn-1
ORDER BY start_date;

SqlFiddleDemo

Output:

╔═══════════════════════════╦═════════════════════════╗
║        start_date         ║        end_date         ║
╠═══════════════════════════╬═════════════════════════╣
║ January, 01 0001 00:00:00 ║ March, 01 2015 00:00:00 ║
║ March,   01 2015 00:00:00 ║ May,   31 2015 00:00:00 ║
║ May,     31 2015 00:00:00 ║ June,  13 2015 00:00:00 ║
║ June,    13 2015 00:00:00 ║ March, 30 2016 11:03:38 ║
╚═══════════════════════════╩═════════════════════════╝

EDIT:

Another possibility is to use LAG/LEAD windowed functions:

SELECT COALESCE(LAG(cleaning) OVER(ORDER BY cleaning), '0001-01-01'::timestamp) 
       AS start_date
      ,cleaning AS end_date
FROM tab
UNION ALL
SELECT MAX(cleaning), CURRENT_TIMESTAMP
FROM tab
ORDER BY start_date;

SqlFiddleDemo2