$('#button').click({
    customData: 'foo'
}, handlerFunction);

function handlerFunction(event) {
    console.log(event.data.customData);
}

function make_event_handler(customData){
    return function(evt){
        //customData can be used here
        //just like any other normal variable
        console.log(customData);
    }
}

dojo.connect(node, 'onclick', make_event_handler(17));

function event_handler(customData, evt){
     ///
}

dojo.connect(node, 'onclick', dojo.partial(event_handler, 17))

this.connect(other, "onClick", function(e) {
    /* other is accesible here still */
});

this.connect(other, "onClick", dojo.hitch(this, "handler", other);

this.handler = function(other, evt){...}