Infinitely many.
Every regular polygon with 2n sides has n pairs of parallel sides. Then there are irregular polygons which can have parallel sides. And there are also irregular shapes which have parallel sides.
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An infinite number of shapes.
all right some body said that Ellipse Circle Oval but parallel shapes need to have lines so they are not parallel shapes so all i know that are not parallel is a diamond and a rhombus
A square or rectangle are the only regular polygons, but many other shapes have two right angles and two parallel lines.
A trapezoid, trapezium and a pentagon have only 1 set of parallel lines.
Rectangles and squares