How can I wait for set of asynchronous callback functions?

You haven’t been very specific with your code, so I’ll make up a scenario. Let’s say you have 10 ajax calls and you want to accumulate the results from those 10 ajax calls and then when they have all completed you want to do something. You can do it like this by accumulating the data in an array and keeping track of when the last one has finished:

Manual Counter

var ajaxCallsRemaining = 10;
var returnedData = [];

for (var i = 0; i < 10; i++) {
    doAjax(whatever, function(response) {
        // success handler from the ajax call

        // save response
        returnedData.push(response);

        // see if we're done with the last ajax call
        --ajaxCallsRemaining;
        if (ajaxCallsRemaining <= 0) {
            // all data is here now
            // look through the returnedData and do whatever processing 
            // you want on it right here
        }
    });
}

Note: error handling is important here (not shown because it’s specific to how you’re making your ajax calls). You will want to think about how you’re going to handle the case when one ajax call never completes, either with an error or gets stuck for a long time or times out after a long time.

jQuery Promises

Adding to my answer in 2014. These days, promises are often used to solve this type of problem since jQuery’s $.ajax() already returns a promise and $.when() will let you know when a group of promises are all resolved and will collect the return results for you:

var promises = [];
for (var i = 0; i < 10; i++) {
    promises.push($.ajax(...));
}
$.when.apply($, promises).then(function() {
    // returned data is in arguments[0][0], arguments[1][0], ... arguments[9][0]
    // you can process it here
}, function() {
    // error occurred
});

ES6 Standard Promises

As specified in kba’s answer: if you have an environment with native promises built-in (modern browser or node.js or using babeljs transpile or using a promise polyfill), then you can use ES6-specified promises. See this table for browser support. Promises are supported in pretty much all current browsers, except IE.

If doAjax() returns a promise, then you can do this:

var promises = [];
for (var i = 0; i < 10; i++) {
    promises.push(doAjax(...));
}
Promise.all(promises).then(function() {
    // returned data is in arguments[0], arguments[1], ... arguments[n]
    // you can process it here
}, function(err) {
    // error occurred
});

If you need to make a non-promise async operation into one that returns a promise, you can “promisify” it like this:

function doAjax(...) {
    return new Promise(function(resolve, reject) {
        someAsyncOperation(..., function(err, result) {
            if (err) return reject(err);
            resolve(result);
        });
    });
}

And, then use the pattern above:

var promises = [];
for (var i = 0; i < 10; i++) {
    promises.push(doAjax(...));
}
Promise.all(promises).then(function() {
    // returned data is in arguments[0], arguments[1], ... arguments[n]
    // you can process it here
}, function(err) {
    // error occurred
});

Bluebird Promises

If you use a more feature rich library such as the Bluebird promise library, then it has some additional functions built in to make this easier:

 var doAjax = Promise.promisify(someAsync);
 var someData = [...]
 Promise.map(someData, doAjax).then(function(results) {
     // all ajax results here
 }, function(err) {
     // some error here
 });

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