Use Select to extract each category of points and then overlay plots of the two categories using Show. You can do that with any number of properties, selections and colors.
yourlist={{-1,3},{2,4},{-2,2},{3,1}};
Show[
ListPlot[Select[yourlist,#[[1]]<0&],PlotStyle->Red],
ListPlot[Select[yourlist,#[[1]]>0&],PlotStyle->Green],
AxesOrigin->{0,0},PlotRange->All
]
