A rectangle or, if the squares are allowed to overlap it is possible to have a 16-gon ("star" shaped), 14-gon, 9-gon, 8-gon.
There are quite a few. Circles, squares, triangles...
a rectangle
A prism.
rectangle
Squares.
When two squares share a common side, they can be combined to form a larger shape known as a rectangle. By aligning the shared side of the squares, the resulting shape will have two pairs of equal sides and four right angles. This new shape will have a different area and perimeter compared to the individual squares.
A cuboid or a rectangular prism.
A triangular prism
Rectangular prism
If the squares can be placed on top of one another, they could form a shape with from 6 to 16 sides.If the squares can be placed on top of one another, they could form a shape with from 6 to 16 sides.If the squares can be placed on top of one another, they could form a shape with from 6 to 16 sides.If the squares can be placed on top of one another, they could form a shape with from 6 to 16 sides.
There is no solid shape with exactly four squares and no other faces.
An isosceles-triangle based prism.