Some 2-dimensional vector fields

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

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

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

A 3-dimensional vector field (unit vectors pointing away from the origin).

VectorPlot3D[ { x/Sqrt[x^2+y^2+z^2], y/Sqrt[x^2+y^2+z^2], z/Sqrt[x^2+y^2+z^2] }, {x,-2,2}, {y,-2,2}, {z,-2,2} ]