Formula in cell E6:

=SUMPRODUCT((B6< =$C$6:$C$12)*(C6>=$B$6:$B$12))>1

Copy cell E6 and paste it down as far as needed.

See an explanation of this formula here:
Highlight overlapping date ranges using conditional formatting in excel

Download excel sample file for this tutorial.
overlapping dates.xls
(Excel 97-2003 Workbook *.xls)

Functions in this article:

SUMPRODUCT(array1, array2, )
Returns the sum of the products of the corresponding ranges or arrays