Solution 1:

There is no 'jQuery' magic, just JavaScript timers.

var pressTimer;

$("a").mouseup(function(){
  clearTimeout(pressTimer);
  // Clear timeout
  return false;
}).mousedown(function(){
  // Set timeout
  pressTimer = window.setTimeout(function() { ... Your Code ...},1000);
  return false; 
});

Solution 2:

Based on Maycow Moura's answer, I wrote this. It also ensures that the user didn't do a right click, which would trigger a long press and works on mobile devices. DEMO

var node = document.getElementsByTagName("p")[0];
var longpress = false;
var presstimer = null;
var longtarget = null;

var cancel = function(e) {
    if (presstimer !== null) {
        clearTimeout(presstimer);
        presstimer = null;
    }

    this.classList.remove("longpress");
};

var click = function(e) {
    if (presstimer !== null) {
        clearTimeout(presstimer);
        presstimer = null;
    }

    this.classList.remove("longpress");

    if (longpress) {
        return false;
    }

    alert("press");
};

var start = function(e) {
    console.log(e);

    if (e.type === "click" && e.button !== 0) {
        return;
    }

    longpress = false;

    this.classList.add("longpress");

    if (presstimer === null) {
        presstimer = setTimeout(function() {
            alert("long click");
            longpress = true;
        }, 1000);
    }

    return false;
};

node.addEventListener("mousedown", start);
node.addEventListener("touchstart", start);
node.addEventListener("click", click);
node.addEventListener("mouseout", cancel);
node.addEventListener("touchend", cancel);
node.addEventListener("touchleave", cancel);
node.addEventListener("touchcancel", cancel);

You should also include some indicator using CSS animations:

p {
    background: red;
    padding: 100px;
}

.longpress {
    -webkit-animation: 1s longpress;
            animation: 1s longpress;
}

@-webkit-keyframes longpress {
    0%, 20% { background: red; }
    100% { background: yellow; }
}

@keyframes longpress {
    0%, 20% { background: red; }
    100% { background: yellow; }
}

Solution 3:

You can use taphold event of jQuery mobile API.

jQuery("a").on("taphold", function( event ) { ... } )

Solution 4:

I created long-press-event (0.5k pure JS) to solve this, it adds a long-press event to the DOM.

Listen for a long-press on any element:

// the event bubbles, so you can listen at the root level
document.addEventListener('long-press', function(e) {
  console.log(e.target);
});

Listen for a long-press on a specific element:

// get the element
var el = document.getElementById('idOfElement');

// add a long-press event listener
el.addEventListener('long-press', function(e) {

    // stop the event from bubbling up
    e.preventDefault()

    console.log(e.target);
});

Works in IE9+, Chrome, Firefox, Safari & hybrid mobile apps (Cordova & Ionic on iOS/Android)

Demo