VectorPlot

VectorPlot[{v_x,v_y},{x,x_min,x_max},{y,y_min,y_max}]

generates a vector plot of the vector field {v_x,v_y} as a function of x and y.

VectorPlot[{{v_x,v_y},{w_x,w_y},…},{x,x_min,x_max},{y,y_min,y_max}]

plots several vector fields.

VectorPlot[…,{x,y}∈reg]

takes the variables {x,y} to be in the geometric region reg.

Details and Options

VectorPlot by default shows vectors from the vector field at a regular grid of positions.
VectorPlot omits any vectors for which the v_i etc. do not evaluate to real numbers.
VectorPlot treats the variables x and y as local, effectively using Block.
VectorPlot has attribute HoldAll, and evaluates the v_i etc. only after assigning specific numerical values to x and y.
In some cases it may be more efficient to use Evaluate to evaluate the v_i etc. symbolically before specific numerical values are assigned to x and y.
VectorPlot has the same options as Graphics, with the following additions and changes:

AspectRatio	1	ratio of height to width
EvaluationMonitor	None	expression to evaluate at every function evaluation
Frame	True	whether to draw a frame around the plot
FrameTicks	Automatic	frame tick marks
Method	Automatic	methods to use for the plot
PerformanceGoal	$PerformanceGoal	aspects of performance to try to optimize
PlotLegends	None	legends to include
PlotRange	{Full,Full}	range of x, y values to include
PlotRangePadding	Automatic	how much to pad the range of values
PlotTheme	$PlotTheme	overall theme for the plot
RegionFunction	True&	determine what region to include
VectorColorFunction	None	how to color vectors
VectorColorFunctionScaling	True	whether to scale the argument to VectorColorFunction
VectorMarkers	Automatic	shape to use for vectors
VectorPoints	Automatic	the number or placement of vectors to plot
VectorScale	Automatic	the scale and size of vectors to plot
VectorStyle	Automatic	how to draw vectors
WorkingPrecision	MachinePrecision	precision to use in internal computations