Pro: Readability

While plenty of people talk about the readability problems with misused ternary operators, there are also situations where using a full if/else would be annoyingly bulky, spreading a simple statement across five lines, and significantly reducing readability. Here are some sample statements pulled from a project I'm working on:

bg_2d.fillStyle = is_in_bounds(x, y) ? grid_colors[x][y] : "#ffffff";

const diagonal_slowdown = is_diagonal() ? Math.SQRT2 : 1;

const color = (team == "red") ? "#ff0000" : "#0000ff";

When you have a simple situation where you have two things to pick from based on a condition, which happens all the time, ternary is perfect. Having a short syntax for ternary massively improves readability in these situations.

This is a one-line shorthand for an if-else statement. It's called the conditional operator.¹

Here is an example of code that could be shortened with the conditional operator:

var userType;
if (userIsYoungerThan18) {
  userType = "Minor";
} else {
  userType = "Adult";
}

if (userIsYoungerThan21) {
  serveDrink("Grape Juice");
} else {
  serveDrink("Wine");
}

This can be shortened with the ?: like so:

var userType = userIsYoungerThan18 ? "Minor" : "Adult";

serveDrink(userIsYoungerThan21 ? "Grape Juice" : "Wine");

Like all expressions, the conditional operator can also be used as a standalone statement with side-effects, though this is unusual outside of minification:

userIsYoungerThan21 ? serveGrapeJuice() : serveWine();

They can even be chained:

serveDrink(userIsYoungerThan4 ? 'Milk' : userIsYoungerThan21 ? 'Grape Juice' : 'Wine');

Be careful, though, or you will end up with convoluted code like this:

var k = a ? (b ? (c ? d : e) : (d ? e : f)) : f ? (g ? h : i) : j;

¹ Often called "the ternary operator," but in fact it's just a ternary operator [an operator accepting three operands]. It's the only one JavaScript currently has, though.

Heh, there are some pretty exciting uses of ternary syntax in your question; I like the last one the best...

x = (1 < 2) ? true : false;

The use of ternary here is totally unnecessary - you could simply write

x = (1 < 2);

Likewise, the condition element of a ternary statement is always evaluated as a Boolean value, and therefore you can express:

(IsChecked == true) ? removeItem($this) : addItem($this);

Simply as:

(IsChecked) ? removeItem($this) : addItem($this);

In fact, I would also remove the IsChecked temporary as well which leaves you with:

($this.hasClass("IsChecked")) ? removeItem($this) : addItem($this);

As for whether this is acceptable syntax, it sure is! It's a great way to reduce four lines of code into one without impacting readability. The only word of advice I would give you is to avoid nesting multiple ternary statements on the same line (that way lies madness!)