Use the in keyword:
"key" in object
which returns true or false, depending if the object, or anything in its prototype chain, has that property.
You can also use object.hasOwnProperty("key"), which will only be true if the object has key as a property of itself, not its prototype. Example:
var object = {};
"toString" in object; // true
object.hasOwnProperty("toString"); // false
Note (as per @dandavis's comment) that if object has a custom property called hasOwnProperty, this gets thwarted; to work around this, use hasOwnProperty.call(object, "key"). Example:
var a = {hasOwnProperty: Boolean};
a.hasOwnProperty('name'); // true
hasOwnProperty.call(a, 'name'); // false