Square is a very interesting format. I feel it gives much more freedom in composition. As 3/4 or 2/3 format have many awkward focus spots, in square it's very hard to find any spots that would be impossible to handle. This is one reason I feel square is a very good format for beginners too.
Square's symmetry is also very appealing and therefore very good for symmetrical compositions and abstracts. I find it also very suitable for street photography, details and textures and for landscapes.
Some examples of square compositions:
Landscape. A tree at Vesijärvi Lake. Lahti, Finland.
And something else...
Now go and make a square!