Interactive 2D Multivariate Normal

In 3D

Needs["MultivariateStatistics`"];
Manipulate[
Plot3D[PDF[MultinormalDistribution[{μ1,μ2},{{σ11,σ12},{σ12,σ22}}],{x,y}],{x,-5,5},{y,-5,5},PlotRange->All,PlotPoints->30],
{{σ11,1},-2,2},{{σ22,1},-2,2}, {{σ12,0},-1,1}, 
{{μ1,0},-3,3},{{μ2,0},-3,3}
]

From Above

Needs["MultivariateStatistics`"];
Manipulate[
ContourPlot[PDF[MultinormalDistribution[{μ1,μ2},{{σ11,σ12},{σ12,σ22}}],{x,y}],{x,-5,5},{y,-5,5},PlotRange->All],
{{σ11,1},-2,2},{{σ22,1},-2,2}, {{σ12,0},-1,1}, 
{{μ1,0},-3,3},{{μ2,0},-3,3}
]

3D Gaussians

data = Table[Flatten[Table[RandomReal[NormalDistribution[0,1],1],{i,1,3}]],{j,1,10000}];
ListPointPlot3D[data]

Plot distribution of distances from the mean

dists = Map[Norm, data];
Histogram[dists]

Distance from Mean

1 Dimension

data = Table[Flatten[Table[RandomReal[NormalDistribution[0,1],1],{i,1,1}]],{j,1,10000}];
dists = Map[Norm,data];
Histogram[dists]

2 Dimensions

data = Table[Flatten[Table[RandomReal[NormalDistribution[0,1],1],{i,1,2}]],{j,1,10000}];
dists = Map[Norm,data];
Histogram[dists]

3 Dimensions

data = Table[Flatten[Table[RandomReal[NormalDistribution[0,1],1],{i,1,3}]],{j,1,10000}];
dists = Map[Norm,data];
Histogram[dists]

20 Dimensions

data = Table[Flatten[Table[RandomReal[NormalDistribution[0,1],1],{i,1,20}]],{j,1,10000}];
dists = Map[Norm,data];
Histogram[dists]