NAME  CITY     DATE
==================================
Paul  Hamburg  01.10.2015 08:00
Jean  Berlin   01.10.2015 12:00
Anne  Munich   02.10.2015 08:00
Peter Cologne  02.10.2015 10:00
Mike  Hamburg  02.10.2015 12:00
John  Berlin   03.10.2015 06:00

NAME  CITY     DATE              ROW_NUM
========================================
Paul  Hamburg  01.10.2015        1
Jean  Berlin   01.10.2015        2 
Anne  Munich   02.10.2015        1        [ <-- New Day: Restart at 1]
Peter Cologne  02.10.2015        2
Mike  Hamburg  02.10.2015        3
John  Berlin   03.10.2015        1        [ <-- New Day: Restart at 1]

  SELECT name,
         city,
         datum,
         ROW_NUMBER () OVER (PARTITION BY TRUNC (datum) ORDER BY datum) rn
    FROM your_table
ORDER BY datum;