2-dimensional random walk

Generate a list of random numbers and Accumulate:

b = Accumulate @ RandomVariate[NormalDistribution[0, 1], 500];

ListLinePlot[b, PlotRange -> 35]

enter image description here

For 2D, you can generate pairs of random numbers and Accumulate:

SeedRandom[1]

b2 = Accumulate @ RandomVariate[NormalDistribution[0, 1], {500, 2}];

ListLinePlot[b2, AspectRatio -> Automatic]

enter image description here

FoldList[Plus, {0, 0}, RandomVariate[NormalDistribution[0, 1], {500, 2}]] // Line // Graphics

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