For any 2-dimensional lattice, the unit cells are parallelograms, which in special cases may have orthogonal angles, equal lengths, or both.  Four of the five two-dimensional Bravais lattices are represented using conventional primitive cells, as shown below. 
The centered rectangular lattice also has a primitive cell in the shape of a rhombus, but in order to allow easy discrimination on the basis of symmetry, it is represented by a conventional cell which contains two lattice points.