cloud.sagemath.com

x,y=var('x y')
plot_vector_field((y,-x),(x,-5,5),(y,-5,5),aspect_ratio=1)
plot_vector_field((cos(x*y),sin(x*y)),(x,0,5),(y,0,5),aspect_ratio=1)
plot_vector_field((cos(x*y),sin(x*y)),(x,3,4),(y,3,4),aspect_ratio=1)
plot_vector_field((4*x**3-8*x,4*y**3-8*y),(x,-5,5),(y,-5,5),aspect_ratio=1)
plot_vector_field((4*x**3-8*x,4*y**3-8*y),(x,-2,2),(y,-2,2),aspect_ratio=1)
plot_vector_field((y,x),(x,-5,5),(y,-5,5),aspect_ratio=1)
plot_vector_field((-y,x),(x,-5,5),(y,-5,5),aspect_ratio=1)


P.S. I figured out that you can actually get Wolfram Alpha
to do vector field plots, just not with a command-line interface.

You first have to enter "vector plot" or similar,
without any accompanying numbers or formulas.
Then you a get a form into which you can enter
the information required.

http://www.wolframalpha.com/input/?i=vector+plot