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Since I do not like the style of the Mathematica plots, I prefer to extract the data points and use other programs to get publish quality plots.

Plot, extract data to a file

In this page, it is explained how to extract data points from already drawn figure in Mathematica. However, this command does not work if the function is piecewise continous. For instance;

data = Cases[Plot[Tan@x, {x, 0, 2 Pi}], Line[data_] :> data, -4, 1][[1]];

Export["file.txt", data, "Table"]

Then the extracted data is up to pi/2 , to the part where the function diverges.

Is there a way to get all the data points that is drawn with Mathematica to get the exact same plot with other programs?

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    $\begingroup$ The plots in Mathematica are extremely customizable. Have you considered tweaking the many formatting options to create a style that suits you or using one of the many build in PlotThemes? These too can be customized through the plot function's options. $\endgroup$ – Edmund Aug 31 '16 at 19:36
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    $\begingroup$ With the possible exception of the typesetting component, I agree with @Edmund. So ... maybe you could post an example of an aesthetic plot that you feel is hard to produce with WL. $\endgroup$ – Alan Aug 31 '16 at 23:40
  • $\begingroup$ This solves my problem. However, is there a way to get the output in the same format? All the x and y values with the same significant figures for instance. $\endgroup$ – sbilmis Sep 2 '16 at 7:44
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In your Cases command you specifically asked for only the first line. You can grab all the lines, and Catenate the results into a single list

data = Catenate@
   Cases[Plot[Tan@x, {x, 0, 2 Pi}], Line[data_] :> data, Infinity];
Export["file.txt", data, "Table"];
ListPlot[Import["file.txt", "Table"]]

Mathematica graphics

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An alternative 

points = Table[{x, Tan[x]}, {x, Range[0, 2 π, .01]}];

ListLinePlot[points]

enter image description here

Shallow[points]

{{0., 0.}, {0.01, 0.0100003}, {0.02, 0.0200027}, {0.03, 0.030009}, {0.04, 0.0400213}, {0.05, 0.0500417}, {0.06, 0.0600721}, {0.07, 0.0701146}, {0.08, 0.0801711}, {0.09, 0.0902438}, <<619>>}

So, points is your List, containing 600plus Values. And you can use your strategy to save'em:

Export["points.txt", points, "Table"]
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    $\begingroup$ Plot chooses its point adaptively, so your method will not yield the same point set. $\endgroup$ – Sjoerd C. de Vries Aug 31 '16 at 19:33

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