Can plain Javascript objects have events?

Not directly but you add the required publish/subscribe infrastructure to any one of them.

No.

However, you could make your own implementation by writing addEventListener and other functions and storing a list of handlers for each event.

For example: (Untested)

function addEventListener(name, handler) {
    if (!this.events) this.events = {};
    if (!this.events[name]) this.events[name] = [];
    this.events[name].push(handler);
}

function removeEventListener(name, handler) {
    if (!this.events) return;
    if (!this.events[name]) return;
    for (var i = this.events[name].length - 1; i >= 0; i--)
        if (this.events[name][i] == handler)
            this.events[name].splice(i, 1);
}

function raiseEvent(name, args) {
    if (!this.events) return;
    if (!this.events[name]) return;
    for (var i = 0; i < this.events[name].length; i++)
        this.events[name][i].apply(this, args);
}


var obj = ...;
obj.addEventListener = addEventListener;
obj.removeEventListener = removeEventListener;
obj.raiseEvent = raiseEvent;

You'll have to implement your own functionality for that, but that's not very hard.

var obj = {
    events: {},
    addEventListener: function(eventName, handler) {
        if(!(eventName in this.events))
            this.events[eventName] = [];

        this.events[eventName].push(handler);
    },

    raiseEvent: function(eventName, args) {
        var currentEvents = this.events[eventName];
        if(!currentEvents) return;

        for(var i = 0; i < currentEvents.length; i++) {
           if(typeof currentEvents[i] == 'function') {
              currentEvents[i](args);
           }
        }
    },

    click: function() {
        // custom 'click' function. when this is called, you do whatever you
        // want 'click' to do. and then raise the event:

        this.raiseEvent('onClick');
    }
};