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Upgrading from:

Graphics`MultipleListPlot`

MultipleListPlot is replaced by ListPlot and ListLinePlot, which now accept multiple sets of data.
Dashing[{Dot,Dash,LongDash}] is replaced with Dashing[{Tiny,Small,Medium,Large}].
A new Error Bar Plots Package has been created.

ListPlot now works with multiple sets of data:

Version 5.2 MultipleListPlot[Range[5], Range[5]^2]
Wolfram Language code: ListPlot[{Range[5], Range[5] ^ 2}]

The new ListPlot option Joined replaces the PlotJoined option to MultipleListPlot:

Version 5.2 MultipleListPlot[Range[5], Range[5]^2, PlotJoined -> {True, False}]
Wolfram Language code: ListPlot[{Range[5], Range[5] ^ 2}, Joined -> {True, False}]

SymbolShape- Stem is replaced by the Filling option to ListPlot:

Version 5.2 MultipleListPlot[Range[5], SymbolShape -> Stem]
Wolfram Language code: ListPlot[Range[5], Filling -> Axis]

Other uses of SymbolShape are replaced by the PlotMarkers option to ListPlot:

Version 5.2 MultipleListPlot[Range[5], SymbolShape -> {PlotSymbol[Triangle], PlotSymbol[Box]}]
Wolfram Language code: ListPlot[{Range[5], Range[5] + 2}, PlotMarkers -> {[image], [image]}]

SymbolLabel->{{labels1},...{labelsn}} can be reproduced by mapping the function Tooltip across the lists:

Version 5.2 MultipleListPlot[Range[4], Range[4] + \[Pi], SymbolLabel -> {Range[4], Range[4] + \[Pi]}]
Wolfram Language code: ListPlot[Map[Tooltip, {Range[4], Range[4] + π}, 2]]

Tiny, Small, Medium, and Large can be used to specify Dashing lengths:

Version 5.2 Graphics[{Dashing[{Dot, Dash, LongDash, Dash}], Line[{{0, 0}, {1, 1}}]}]
Wolfram Language code: Graphics[{Dashing[{Tiny, Medium, Large, Medium}], Line[{{0, 0}, {1, 1}}]}]

ErrorBar and related styling options are now found in the Error Bar-Plots Package:

Wolfram Language code: <<ErrorBarPlots`
Wolfram Language code: ErrorListPlot[{{{1, 2}, ErrorBar[0.3]}, {{2, 3}, ErrorBar[0.3]}, {{3, 6}, ErrorBar[{-0.1, 0.5}]}, {{6, 2}, ErrorBar[{-0.2, 0.1}, {-0.5, 0.8}]}} ]

RegularPolygon can be replaced by the following simple definition:

Wolfram Language code: RegularPolygon[n_, rad_ : 1, ctr_ : {0, 0}, tilt_ : 0, k_ : 1] := Line[ Table[ctr + rad{Cos[t + tilt], Sin[t + tilt]}, {t, 0, 2Pi, 2Pi / n}][[NestList[Mod[# + k, n, 1]&, 1, n]]] ] ; Graphics[RegularPolygon[7, 1, {0, 0}, 0, 3]]

MakeSymbol was available in previous versions of Mathematica and is now available on the web at library.wolfram.com/infocenter/MathSource/6819.