If you want the labels to be retained for the tooltip, but not displayed below the bars the following hack might be useful. I made this change for use on an private intranet application and have not tested it for efficiency or side-effects, but it did what I needed.

At about line 71 in chart.js add a property to hide the bar labels:

// Boolean - Whether to show x-axis labels
barShowLabels: true,

At about line 1500 use that property to suppress changing this.endPoint (it seems that other portions of the calculation code are needed as chunks of the chart disappeared or were rendered incorrectly if I disabled anything more than this line).

if (this.xLabelRotation > 0) {
    if (this.ctx.barShowLabels) {
        this.endPoint -= Math.sin(toRadians(this.xLabelRotation)) * originalLabelWidth + 3;
    } else {
        // don't change this.endPoint
    }
}

At about line 1644 use the property to suppress the label rendering:

if (ctx.barShowLabels) {    
    ctx.fillText(label, 0, 0);
}

I'd like to make this change to the Chart.js source but aren't that familiar with git and don't have the time to test rigorously so would rather avoid breaking anything.

The simplest solution is:

scaleFontSize: 0

see the chart.js Document

smilar question

Inspired by christutty's answer, here is a solution that modifies the source but has not been tested thoroughly. I haven't had any issues yet though.

In the defaults section, add this line around line 71:

// Boolean - Omit x-axis labels
omitXLabels: true,

Then around line 2215, add this in the buildScale method:

//if omitting x labels, replace labels with empty strings           
if(Chart.defaults.global.omitXLabels){
    var newLabels=[];
    for(var i=0;i<labels.length;i++){
        newLabels.push('');
    }
    labels=newLabels;
}

This preserves the tool tips also.

For those whom this did not work, here is how I hid the labels on the X-axis-

options: {
    maintainAspectRatio: false,
    layout: {
      padding: {
        left: 1,
        right: 2,
        top: 2,
        bottom: 0,
      },
    },
    scales: {
      xAxes: [
        {
          time: {
            unit: 'Areas',
          },
          gridLines: {
            display: false,
            drawBorder: false,
          },
          ticks: {
            maxTicksLimit: 7,
            display: false, //this removed the labels on the x-axis
          },
          'dataset.maxBarThickness': 5,
        },
      ],

Faced this issue of removing the labels in Chartjs now. Looks like the documentation is improved. http://www.chartjs.org/docs/#getting-started-global-chart-configuration

Chart.defaults.global.legend.display = false;

this global settings prevents legends from being shown in all Charts. Since this was enough for me, I used it. I am not sure to how to avoid legends for individual charts.

(this question is a duplicate of In chart.js, Is it possible to hide x-axis label/text of bar chart if accessing from mobile?) They added the option, 2.1.4 (and maybe a little earlier) has it

var myLineChart = new Chart(ctx, {
    type: 'line',
    data: data,
    options: {
        scales: {
            xAxes: [{
                ticks: {
                    display: false
                }
            }]
        }
    }
}

This is for chart.js ^3.0.0

Remove x-axis labels and grid chart lines

var chart = new Chart(ctx, {
    ...
    options:{
        scales:{
            x: {
                display: false
            }
        }
    }
});

Remove only x-axis labels

var chart = new Chart(ctx, {
    ...
    options: {
        scales: {
            x: {
               ticks: {
                   display: false
              }
           }
        }
    }
});

UPDATE chart.js 2.1 and above

var chart = new Chart(ctx, {
    ...
    options:{
        scales:{
            xAxes: [{
                display: false //this will remove all the x-axis grid lines
            }]
        }
    }
});


var chart = new Chart(ctx, {
    ...
    options: {
        scales: {
            xAxes: [{
                ticks: {
                    display: false //this will remove only the label
                }
            }]
        }
    }
});

Reference: chart.js documentation

Old answer (written when the current version was 1.0 beta) just for reference below:

To avoid displaying labels in chart.js you have to set scaleShowLabels : false and also avoid to pass the labels:

<script>
    var options = {
        ...
        scaleShowLabels : false
    };
    var lineChartData = {
        //COMMENT THIS LINE TO AVOID DISPLAYING THE LABELS
        //labels : ["1","2","3","4","5","6","7"],
        ... 
    }
    ...
</script>