There are total of 40 squares.

How?
Let’s assume the smallest square side is 0.5cm in length.

Now count the squares with different length :-
0.5cm : 8
1cm : 16 +2(in the middle)
2cm : 9
3cm : 4
4cm : 1
————
Total : 40

There are total of 16 squares.
How?

Lets count…
Squares with side length equal to 1 matchstick: 9
Squares with side length equal to 2 matchsticks: 5(2+1+2)
Square with side length equal to 3 matchsticks: 1 (This is difficult to find, and easy to miss)
Square with side length equal to 4 matchsticks: 1 (Everybody knows)
So total number of squares : 16

This image(courtsey Charles on facebook) explains it all:-