Edit in JSFiddle

var oldValueBinding = ko.bindingHandlers['value'];
ko.bindingHandlers['value'] = {
    'init': function (element, valueAccessor, allBindingsAccessor) {

        // If `checked` binding is present, ignore this binding because
        // user wishes to bind the checked value to the model value
        var allBindings = allBindingsAccessor(),
            hasChecked  = allBindings.hasOwnProperty("checked");

        if (hasChecked) {
            return;
        }

        oldValueBinding['init'].apply(this, arguments);
    },
    'update': function (element, valueAccessor, allBindingsAccessor) {
        // If `checked` binding is present, ignore this binding because
        // user wishes to bind the checked value to the model value
        var allBindings = allBindingsAccessor(),
            hasChecked  = allBindings.hasOwnProperty("checked");

        if (hasChecked) {
            return;
        }

        oldValueBinding['update'].apply(this, arguments);
    }
};

ko.bindingHandlers['checked'] = {
    'init': function (element, valueAccessor, allBindingsAccessor) {
        var updateHandler = function() {
            var valueToWrite;
            if (element.type == "checkbox") {
                valueToWrite = element.checked;
            } else if ((element.type == "radio") && (element.checked)) {
                valueToWrite = element.value;
            } else {
                return; // "checked" binding only responds to checkboxes and selected radio buttons
            }

            var modelValue = valueAccessor(), unwrappedValue = ko.utils.unwrapObservable(modelValue),
                allBindingsValue = allBindingsAccessor();
            if ((element.type == "checkbox") && (unwrappedValue instanceof Array)) {
                // For checkboxes bound to an array, we add/remove the checkbox value to that array
                // This works for both observable and non-observable arrays
                var boundValue = (allBindingsValue.hasOwnProperty("value") && ko.utils.unwrapObservable(allBindingsValue.value)) || element.value;

                var existingEntryIndex = ko.utils.arrayIndexOf(unwrappedValue, boundValue);
                if (element.checked && (existingEntryIndex < 0))
                    modelValue.push(boundValue);
                else if ((!element.checked) && (existingEntryIndex >= 0))
                    modelValue.splice(existingEntryIndex, 1);
            } else {
                ko.expressionRewriting.writeValueToProperty(modelValue, allBindingsAccessor, 'checked', valueToWrite, true);
            }
        };
        ko.utils.registerEventHandler(element, "click", updateHandler);

        // IE 6 won't allow radio buttons to be selected unless they have a name
        if ((element.type == "radio") && !element.name)
            ko.bindingHandlers['uniqueName']['init'](element, function() { return true });
    },
    'update': function (element, valueAccessor, allBindingsAccessor) {
        var value = ko.utils.unwrapObservable(valueAccessor()),
            allBindingsValue = allBindingsAccessor();

        if (element.type == "checkbox") {
            if (value instanceof Array) {
                var boundValue = (allBindingsValue.hasOwnProperty("value") && ko.utils.unwrapObservable(allBindingsValue.value)) || element.value;

                // When bound to an array, the checkbox being checked represents its value being present in that array
                element.checked = ko.utils.arrayIndexOf(value, boundValue) >= 0;
            } else {
                // When bound to anything other value (not an array), the checkbox being checked represents the value being trueish
                element.checked = value;
            }
        } else if (element.type == "radio") {
            element.checked = (element.value == value);
        }
    }
};

window.vm = {
        selectedItems: ko.observableArray([]),    
        items: ko.observableArray([
          { id: 1, name: "Foo" },
          { id: 2, name: "Foo2" }
        ])    
    };

    // // Ah. Much better!
    vm.isItem1Selected = ko.computed(function () {
        return this.selectedItems.indexOf(1) > -1;
    }, vm);

    // debug
    vm.model = ko.computed(function () {
        var js = ko.toJS(this);

        delete js.model;

        return ko.toJSON(js);
    }, vm);

    ko.applyBindings(vm);

<h1>Better Checked Binding</h1>

    <ul data-bind="foreach: items">
        <li><input type="checkbox" data-bind="checked: $parent.selectedItems, value: id"> <input type="text" data-bind="value: name"> <span data-bind="text: name"></span></li>
    </ul>

    <strong>Item 1 selected? <span data-bind="text: isItem1Selected"></span></strong>

    <pre data-bind="text: model"></pre>