jmc

To start, we can clearly draw $1\times 1$,$2\times 2$,$3\times 3$,and $4\times 4$ squares. Next, we must consider the diagonals. We can draw squares with sides of $\sqrt{2}$ and $2\sqrt{2}$ as shown: In addition, we can draw squares with side lengths diagonals of $1\times 2$ and $1\times 3$ rectangles as shown: Any larger squares will not be able to fit on the lattice. There are a total of $4+2+2=\boxed{8}$ possible squares.