For regular polygons: 3, 4, or 6.
For irregular polygons, figures with any number of sides can be found.
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A compass and straight edge are used to create a polygon but do not limit the number of sides of the polygon created. You have to decide that separately, then use the compass and straight edge to make what you decide on.
You can use the formula D=S-2 where D is the number of possible diagonals and S is the number of sides the polygon has.
It is used in the formula for finding the sum of the interior angles of a polygon:- (n-2)*180 = sum of interior angles whereas 'n' is the number of sides of the polygon
Let S be the sum of the measures of all the interior angles, in degrees. Then the number of sides is S/180 + 2.
Limited only by the media used to draw it! It can, of course, go critical and be indistinguishable from a circle!