myArray.sort(
  function(a, b) {
    if (a.toLowerCase() < b.toLowerCase()) return -1;
    if (a.toLowerCase() > b.toLowerCase()) return 1;
    return 0;
  }
);

编辑: 请注意，我最初写这篇文章是为了说明技术，而不是考虑性能。也请参考回答@Ivan Krechetov更紧凑的解决方案。

ES6版本:

["Foo", "bar"].sort(Intl.Collator().compare)

来源:https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Collator/compare

如果你在努力理解以下内容，这可能会有所帮助:

var array = ["sort", "Me", "alphabetically", "But", "Ignore", "case"];
console.log('Unordered array ---', array, '------------');

array.sort(function(a,b) {
    a = a.toLowerCase();
    b = b.toLowerCase();
    console.log("Compare '" + a + "' and '" + b + "'");

    if( a == b) {
        console.log('Comparison result, 0 --- leave as is ');
        return 0;
    }
    if( a > b) {
        console.log('Comparison result, 1 --- move '+b+' to before '+a+' ');
        return 1;
    }
    console.log('Comparison result, -1 --- move '+a+' to before '+b+' ');
    return -1;


});

console.log('Ordered array ---', array, '------------');


// return logic

/***
If compareFunction(a, b) is less than 0, sort a to a lower index than b, i.e. a comes first.
If compareFunction(a, b) returns 0, leave a and b unchanged with respect to each other, but sorted with respect to all different elements. Note: the ECMAscript standard does not guarantee this behaviour, and thus not all browsers (e.g. Mozilla versions dating back to at least 2003) respect this.
If compareFunction(a, b) is greater than 0, sort b to a lower index than a.
***/

http://jsfiddle.net/ianjamieson/wmxn2ram/1/

其他答案假设数组包含字符串。我的方法更好，因为即使数组包含null、undefined或其他非字符串，它也能工作。

var notdefined;
var myarray = ['a', 'c', null, notdefined, 'nulk', 'BYE', 'nulm'];

myarray.sort(ignoreCase);

alert(JSON.stringify(myarray));    // show the result

function ignoreCase(a,b) {
    return (''+a).toUpperCase() < (''+b).toUpperCase() ? -1 : 1;
}

null将在'nulk'和'nulm'之间排序。但未定义的总是排在最后。

在/ /i中包装字符串。这是使用正则表达式忽略大小写的一种简单方法

如果不管输入数组中元素的顺序如何，你都想保证相同的顺序，这里是一个稳定排序:

myArray.sort(function(a, b) {
    /* Storing case insensitive comparison */
    var comparison = a.toLowerCase().localeCompare(b.toLowerCase());
    /* If strings are equal in case insensitive comparison */
    if (comparison === 0) {
        /* Return case sensitive comparison instead */
        return a.localeCompare(b);
    }
    /* Otherwise return result */
    return comparison;
});