Generate a list of random numbers and Accumulate:
b = Accumulate @ RandomVariate[NormalDistribution[0, 1], 500]; ListLinePlot[b, PlotRange -> 35] 
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] 