Assuming that your sample data table is in cells A1 to C9
then you can achieve the following:
A B C D
11 Date 01/01/10 01/02/10 01/03/10
13 A 0 2 5
14 B 60 0 0
15 C 800 55 60
Enter the following formula in cell B13:
Drag to extend the formula through to cell D15
Note the $ signs - they are essential for the formula to be extended properly by dragging or copy/pasting.
From what you said, I assumed that you wanted the total counts not just 1 or 0 as shown in your post. If you wanted to return zero if the count was zero, or 1 if the count was not zero, let me know and the formula can be modified.
Without having real data to work on I cannot test that this will work with your data. If it does not work 'as expected' please post some real data with the expected results, and information on what was returned by the above formula.
It may be better to format dates with text for the month, to help ensure that apparently similar dates are actually the same.
1/2/10 : 01 Feb 2010 or 02 Jan 2010