var myView = Backbone.view.extend({
    events: {'click .myClass': 'myFunction'},
    initialze: //initialize function,
    render: //render function,
    myFunction: function (e) {
        //do something
    }
});

var myView = Backbone.view.extend({
    events: {'click .myClass': 'myFunction'},
    initialze: //initialize function,
    render: //render function,
    myFunction: function (e) {
        if(e.target.getAttribute("data-fired")) return;
        e.target.setAttribute("data-fired", true);
        // Do your stuff
    }
});

var myView = Backbone.view.extend({
    events: {
        'click .myClass': 'myFunction'
    },
    initialze: //initialize function,
    render: //render function,
    myFunction: function (e) {
        if (e.target.className.search(/triggered/) !== -1) return; // event already triggered once
        e.target.className += "triggered";
        //do something when its triggered first time
    }
});

Backbone.View.extend({
    events: {
        'click .myClass.onlyOnce': 'doThings'
    },
    doThings: function(e) {
        $(e.currentTarget).removeClass('onlyOnce');
        //...
    },
    //...
});