Plotting a 2-dimensional vector field. The field in question is a classic radial field.

VectorPlot[ {x, y}, {x,-2,2},{y,-2,2} ]

Another 2-dimensional plot, this time of a classic rotational vector field.

VectorPlot[ {-y, x}, {x,-2,2},{y,-2,2}]

A 3-dimensional vector field, with both radial and rotational features (vector fields don’t have to be solely one or the other). This field is rotational around the z axis, but has a radial component in the z direction.

VectorPlot3D[ { -y, x, z}, {x,-2,2}, {y,-2,2}, {z,-2,2}  ]

Another 3-dimensional field that is purely rotational. It also demonstrates that component functions can be constants, such as the z component that’s always 0 in this field.

VectorPlot3D[ { -y, x, 0}, {x,-2,2}, {y,-2,2}, {z,-2,2}  ]

A 3-dimensional field that has more complicated component functions.

VectorPlot3D[ { Cos[x], Sin[y], z}, {x,-2*Pi,2*Pi}, {y,-2*Pi,2*Pi}, {z,-2*Pi,2*Pi}  ]