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One possible method of systematically counting the rectangles it to start by looking at all of the points that could be the top left corner of a rectangle. These have been numbered working from top left to bottom right.
Now take each of these 'corners' in turn and count how many rectangles can be found containing this corner at the top left. The results are shown in the table below:
Corner  Number of rectangles  View rectangles 
1  1  
2  3  
3  2  
4  3  
5  1  
6  5  
7  3  
8  2  
9  2  
10  2  
11  1  
12  1  
Total:  26 
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Here a concise URL for a version of this page without the comments.
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Here is the URL which will take them to another systematic listing activity.
Other shape counting starters:
How Many Squares 1?
 How Many Squares 2?
How Many Triangles 1?

How Many Triangles 2?  How Many Triangles 3?
How Many Rectangles?
 Rectangles Investigation 
Icosahedron