Full code after the jump.

View MXML

<?xml version="1.0" encoding="utf-8"?>
<!-- http://blog.flexexamples.com/2007/08/30/toggling-resizable-columns-in-a-flex-datagrid-control/ -->
<mx:Application xmlns:mx="http://www.adobe.com/2006/mxml"
        layout="vertical"
        verticalAlign="middle"
        backgroundColor="white">

    <mx:Array id="arr">
        <mx:Object label="User 1" data="1" />
        <mx:Object label="User 2" data="2" />
        <mx:Object label="User 3" data="3" />
        <mx:Object label="User 4" data="4" />
        <mx:Object label="User 5" data="5" />
        <mx:Object label="User 6" data="6" />
        <mx:Object label="User 7" data="7" />
        <mx:Object label="User 8" data="8" />
    </mx:Array>

    <mx:ApplicationControlBar dock="true">
        <mx:CheckBox id="resizableColumnsCh"
                label="resizableColumns"
                selected="true" />

        <mx:CheckBox id="labelResizableCh"
                label="label.resizable"
                selected="true" />

        <mx:CheckBox id="dataResizableCh"
                label="data.resizable"
                selected="true" />
    </mx:ApplicationControlBar>

    <mx:DataGrid id="dataGrid"
            resizableColumns="{resizableColumnsCh.selected}"
            dataProvider="{arr}">
        <mx:columns>
            <mx:DataGridColumn dataField="label"
                    resizable="{labelResizableCh.selected}" />
            <mx:DataGridColumn dataField="data"
                    resizable="{dataResizableCh.selected}" />
        </mx:columns>
    </mx:DataGrid>

</mx:Application>

View source is enabled in the following example.

If you want to detect when a data grid column has been resized, you can listen for the columnStretch event on the DataGrid control, as seen in the following example:

View MXML

<?xml version="1.0" encoding="utf-8"?>
<!-- http://blog.flexexamples.com/2007/08/30/toggling-resizable-columns-in-a-flex-datagrid-control/ -->
<mx:Application xmlns:mx="http://www.adobe.com/2006/mxml"
        layout="horizontal"
        verticalAlign="middle"
        backgroundColor="white">

    <mx:Script>
        <![CDATA[
            import mx.controls.dataGridClasses.DataGridColumn;
            import mx.controls.DataGrid;
            import mx.events.DataGridEvent;

            private function dataGrid_columnStretch(evt:DataGridEvent):void {
                var dg:DataGrid = DataGrid(evt.currentTarget);
                var column:DataGridColumn = dg.columns[evt.columnIndex];
                debug.text += evt.dataField + " == " + column.width + "px" + "\\n";
            }
        ]]>
    </mx:Script>

    <mx:Array id="arr">
        <mx:Object label="User 1" data="1" />
        <mx:Object label="User 2" data="2" />
        <mx:Object label="User 3" data="3" />
        <mx:Object label="User 4" data="4" />
        <mx:Object label="User 5" data="5" />
        <mx:Object label="User 6" data="6" />
        <mx:Object label="User 7" data="7" />
        <mx:Object label="User 8" data="8" />
    </mx:Array>

    <mx:DataGrid id="dataGrid"
            dataProvider="{arr}"
            columnStretch="dataGrid_columnStretch(event)">
        <mx:columns>
            <mx:DataGridColumn dataField="label" />
            <mx:DataGridColumn dataField="data" />
        </mx:columns>
    </mx:DataGrid>

    <mx:TextArea id="debug"
            width="{dataGrid.width}"
            height="{dataGrid.height}" />

</mx:Application>

View source is enabled in the following example.