newlines character ignored by jsx table

You've got a few options:

1) Use a block level element such as div or a p and wrap each line.

var TextLines = React.createClass({      
    render: function() {
        var lines = this.props.lines;

        var formatted = lines.map(function(line) {
            return (<p>{line}</p>);
        });
        return (<div>{ formatted }</div>);
    }
});

var lines = ['line 1', 'line 2', 'line 3'];
React.render(<TextLines lines={ lines }/>, 
              document.getElementById('container'));

2) Use a span with a br element:

var TextLines = React.createClass({      
    render: function() {
        var lines = this.props.lines;

        var br = lines.map(function(line) {
            return (<span>{line}<br/></span>);
        });
        return (<div>{ br }</div>);
    }
});

var lines = ['line 1', 'line 2', 'line 3'];
React.render(<TextLines lines={ lines } />,  
              document.getElementById('container'));

3) If you're certain there is no threat of XSS/hacks with the data, you could use dangerouslySetInnerHTML with a 'br' for each line:

var TextLines = React.createClass({      
    render: function() {
        var lines = this.props.lines;
        var content = {
            __html: lines.join('<br />')
        };     
        return (<div dangerouslySetInnerHTML={ content } />);
    }
});

var lines = ['line 1', 'line 2', 'line 3'];
React.render(<TextLines lines={ lines } />, 
             document.getElementById('container'));

The last one produces the least amount of HTML, but at a cost of potentially risky the security of the web page/user. I wouldn't use this one if the others work for you.

When you really need this, use {'\n'} inside your JSX.

Try white-space: pre; or white-space: pre-wrap; (Thanks, @Mirage) in the style of your cell.

td {
  width: 150px;
}

.nopre {
  background-color: lightblue;
}

.withpre {
  background-color: lightgreen;
  white-space: pre;
}

.withprewrap {
  background-color: orange;
  white-space: pre-wrap;
}

<table><tr>

<td class="nopre">Line A
Line B
Line C
This is a cell with no whitespace setting</td>

</tr></table><table><tr>

<td class="withpre">Line 1
Line 2
Line 3
This is a cell with white-space: pre</td>

</tr></table><table><tr>
  
<td class="withprewrap">Line 1
Line 2
Line 3
This is a cell with white-space: pre-wrap</td>
  
</tr></table>