score:89

Accepted answer

Set dataLabels.styles.textShadow to false.

    plotOptions: {
        columnrange: { // or general options: "series: { ... }"
            dataLabels: {
                enabled: true,
                color: 'red',
                style: {
                    textShadow: false 
                }
            }
        }
    },

Demo: http://jsfiddle.net/oe1vcmqj/2/

EDIT:

Since Highcharts 5.0.3, the option name is textOutline.

    plotOptions: {
        columnrange: { // or general options: "series: { ... }"
            dataLabels: {
                enabled: true,
                color: 'red',
                style: {
                    textOutline: false 
                }
            }
        }
    },

Demo: http://jsfiddle.net/oe1vcmqj/49/

EDIT v2.0:

Since Highcharts 5.0.13, the textOutline option should be a string, so to disable outline, set textOutline: 'none'.

    plotOptions: {
        columnrange: { // or general options: "series: { ... }"
            dataLabels: {
                enabled: true,
                color: 'red',
                style: {
                    textOutline: 'none' 
                }
            }
        }
    },

Demo: http://jsfiddle.net/BlackLabel/s7ejvhmu/

score:0

In version 1.4.0

use

dataLabels: {
  dropShadow: false
}

score:1

worked for me...

dataLabels: {
                enabled: true,
                color: 'white',
                style: {
                    // textShadow: false 
                    textOutline: false
                }

score:2

use text-shadow:none !important; for the tag tspan

CSS

tspan{
    text-decoration:none;
    text-shadow:none !important;
}

FIDDLE DEMO

score:4

dataLabels: {
      enabled: true,
      format: '{point.y}',
       style: {
          textOutline: false 
           }
        },

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