React (Facebook): managed state of controlled checkboxes

In your render function, the scope of this for the checks mapping function is different from render, which is the scope you need for __changeSelection, so this.__changeSelection won’t locate a __changeSelection property. If you add a .bind(this) to the end of that mapping function, you can bind it’s scope to the same this as render:

var checks = this.state.data.map(function(d) {
    return (
        <div>
            <input type="checkbox" data-id={d.id} checked={d.selected} onChange={this.__changeSelection} />
            {d.id}
            <br />
        </div>
    );
}.bind(this));

On a side note, I would just pass the id to the handler function instead of assigning data-attributes. This will remove the need to locate that element in your handler:

var checks = this.state.data.map(function(d) {
    return (
        <div>
            <input type="checkbox" checked={d.selected} onChange={this.__changeSelection.bind(this, d.id)} />
            {d.id}
            <br />
        </div>
    );
}.bind(this));

Then update your __changeSelection function to pass in the id as the first arg and remove the attribute lookup line:

__changeSelection: function(id) {
    var state = this.state.data.map(function(d) {
        return {
            id: d.id,
            selected: (d.id === id ? !d.selected : d.selected)
        };
    });

    this.setState({ data: state });

}

Here is an example of it all put together, along with a jsfiddle for you to try it out:

/** @jsx React.DOM */

var Test = React.createClass({
    getInitialState: function() {
        return {
            data: [
                { id: 1, selected: false },
                { id: 2, selected: false },
                { id: 3, selected: false },
                { id: 4, selected: false }
            ]
        };
    },
    render: function() {
        var checks = this.state.data.map(function(d) {
            return (
                <div>
                    <input type="checkbox" checked={d.selected} onChange={this.__changeSelection.bind(this, d.id)} />
                    {d.id}
                    <br />
                </div>
            );
        }.bind(this));
        return (
            <form>
                <input type="checkbox" ref="globalSelector" onChange={this.__changeAllChecks} />Global selector
                <br />
                {checks}
            </form>
        );
    },
    __changeSelection: function(id) {
        var state = this.state.data.map(function(d) {
            return {
                id: d.id,
                selected: (d.id === id ? !d.selected : d.selected)
            };
        });

        this.setState({ data: state });

    },
    __changeAllChecks: function() {
        var value = this.refs.globalSelector.getDOMNode().checked;
        var state = this.state.data.map(function(d) {
            return { id: d.id, selected: value };
        });

        this.setState({ data: state });
    }
});

React.renderComponent(<Test />, document.getElementById('content'));