There are many ways, I will show one of them. Let a random process be described by a function

matRealizations = 
  Table[Sin[RandomReal[-1, 1] t + RandomReal[]], {81}];

You can display them all together or selectively

Show[Table[
  Plot[matRealizations[[i]], {t, -Pi, Pi}, PlotStyle -> Hue[i/81], 
   PlotRange -> {-1, 1}], {i, 1, 81, 1}]]
{Show[Table[
   Plot[matRealizations[[i]], {t, -Pi, Pi}, PlotStyle -> Hue[i/81], 
    PlotRange -> {-1, 1}], {i, 1, 7, 1}]], 
 Show[Table[
   Plot[matRealizations[[i]], {t, -Pi, Pi}, PlotStyle -> Hue[i/81], 
    PlotRange -> {-1, 1}], {i, {1, 5, 61, 70}}]]}

Hi Jamie,

What is the structure of matRealizations? If it is a list of numbers or a list of lists of points then this should work.

ListPlot[matRealizations, Joined -> True]

If not, you can always generate the list using Table.

ListPlot[Table[matRealizations[[i]], {i, 81}], Joined -> True]