How do I add error bars to my plots?

Mathematica offers a number of powerful functions for presenting experimental error and drawing error bars. The two main ones are ErrorListPlot in the Graphics`Graphics` package and ErrorBar in the MultipleListPlot package. Both packages ship with Mathematica. 
ErrorBar is the much more powerful function and it is well documented in the MultipleListPlot package. So the discussion here is limited to the simpler ErrorListPlot.

Data with explicit y errors

The ErrorListPlot function in the Graphics`Graphics` package, which comes with every copy of Mathematica plots simple {x,y, error} datasets.

Load the package using << or Needs[].

<< Graphics`Graphics`

Here is a sample of experimental data. It is organized in {x, y, error} form.

erexpdata = {{0.2,1.47182,1.},{0.3,1.3549,1.},{0.4,2.60843,1.},{0.5,2.22883,1.},{0.6,4.03274,1.},{0.7,5.1723,1.},{0.8,4.54913,1.},{0.9,6.79017,1.},{1.,8.1925,1.},{1.1,9.83144,1.},{1.2,12.2536,1.}};

Here is a plot of the data in expdata with error bars.

ErrorListPlot[erexpdata, AxesOrigin->{0,0},PlotRange->{{0,1.2},{0,14}}]

Data with calculated errors

ErrorListPlot can also easily deal with dynamically calculated errors, such a percentage of the y-value.

data = {{0.0955879, 0.963101}, {0.158054, 0.729302}, {0.195862, 
            0.693531}, {0.231488, 1.17862}, {0.333678, 1.33753}, {0.437003, 
            1.18039}, {0.586503, 1.39057}, {0.624139, 2.39847}, {0.761755, 
            2.449}, {0.890954, 2.35869}, {0.979321, 2.52493}, {1.12513, 
            3.39772}, {1.18373, 3.76367}, {1.36708, 3.83872}, {1.48787, 
            4.42662}, {1.53559, 4.22235}, {1.65419, 4.87875}, {1.69859, 
            5.08294}, {1.76769, 5.80691}, {1.87445, 6.51017}, {1.90594, 
            7.52287}};

Load the package is you havn't already done so.

<< Graphics`Graphics`

ErrorListPlot[
        Table[{data[[i, 1]], data[[i, 2]], 
            data[[i, 2]]*0.07}, {i, 1, Length[data]}]];