Highcharts 3.0.1
Users can use the highcharts plugin
var chart=$("#container").highcharts();
Highcharts 2.3.4
Read from the Highcharts.charts array, for version 2.3.4 and later, the index of the chart can be found from the data on the <div>
var index=$("#container").data('highchartsChart');
var chart=Highcharts.charts[index];
All versions
Track charts in a global object/map by container id
var window.charts={};
function foo(){
new Highcharts.Chart({...},function(chart){
window.charts[chart.options.chart.renderTo] = chart;
});
}
function bar(){
var chart=window.charts["containerId"];
}
Read Mode @ Highcharts Tips - Accessing Chart Object From a Container ID
P.S.
Some additions were made in the newer versions of Highcharts since writing this answer and have been taken from answers from @davertron, @Moes and @Przy, please upvote their comments/answers as they deserve the credit for these. Adding them here as this accepted answer would be incomplete without these
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