Edit in JSFiddle

     <h1>O's & X's</h1>

    <table>
        <tr>
            <td id="cell0">&nbsp;</td>
            <td id="cell1">&nbsp;</td>
            <td id="cell2">&nbsp;</td>
        </tr>
        <tr>
            <td id="cell3">&nbsp;</td>
            <td id="cell4">&nbsp;</td>
            <td id="cell5">&nbsp;</td>
        </tr>
        <tr>
            <td id="cell6">&nbsp;</td>
            <td id="cell7">&nbsp;</td>
            <td id="cell8">&nbsp;</td>
        </tr>
    </table>
    <p>
        <input type="button" id="btnNewGame" value="New Game" />
    </p>

body {
    background-color: white;
    color: black;
    font-family: Arial, Helvetica, sans-serif;
}
h1 {
    font-size: 28px;
}
table {
    border-collapse: collapse;
}
td {
    padding: 10px;
    border: 3px #888 solid;
    text-align: center;
    font-size: 28px;
    width: 20%;
    font-family: Consolas, monospace
}
/* Set the border (top, right, bottom, left) of the cells */
 #cell0 {
    border-style: none solid solid none;
}
#cell1 {
    border-style: none solid solid solid;
}
#cell2 {
    border-style: none none solid solid;
}
#cell3 {
    border-style: solid solid solid none;
}
#cell4 {
    border-style: solid solid solid solid;
}
#cell5 {
    border-style: solid none solid solid;
}
#cell6 {
    border-style: solid solid none none;
}
#cell7 {
    border-style: solid solid none solid;
}
#cell8 {
    border-style: solid none none solid;
}
/* winning cells style */
 .winningCell {
    background-color: #f88;
}

/*
 * The cells are numbered from 0 to 8 from top-left to bottom-right.
 */

window.onload = init; // run init() after the page is loaded

const NUM_CELLS = 9;

// A pattern is a 9-bit number where bit x represents cell x.
const WINNING_PATTERNS = new Array(0007, 0070, 0700, 0444, 0222, 0111, 0421, 0124); // Octal
var crossPattern, noughtPattern; // keep the plays so far

// "cross" is currently playing (boolean of true or false)
var crossPlaying;

// Initialize the game
function init() {
    resetGame();
    document.getElementById("btnNewGame").onclick = resetGame;
}

// Reset game by clearing all the cells and player's pattern
function resetGame() {
    crossPattern = 0;
    noughtPattern = 0;
    crossPlaying = true;
    for (var cellNum = 0; cellNum < NUM_CELLS; cellNum++) {
        var elm = document.getElementById("cell" + cellNum);
        elm.innerHTML = "&nbsp;"; // Clear content
        elm.className = ""; // Reset the class, used by CSS
        elm.onmousedown = play; // Attach mouse click handler
    }
}

// Mouse-click handler
function play(evt) {
    var thisCell;
    if (evt) { // non-IE
        thisCell = evt.target;
    } else { // IE
        thisCell = window.event.srcElement;
    }

    // Place the seed on the cell clicked and update the player's pattern
    if (thisCell.innerHTML === "&nbsp;") {
        if (crossPlaying) {
            thisCell.innerHTML = "x";
            crossPattern |= Math.pow(2, thisCell.id.charAt(4));
        } else {
            thisCell.innerHTML = "o";
            noughtPattern |= Math.pow(2, thisCell.id.charAt(4));
        }
    }
    if (!checkWin()) {
        // Continue playing
        // Disable mouse click for this cell. This cell is no longer active
        thisCell.onmousedown = null;
        // toggling the current player
        crossPlaying = !crossPlaying;
    }
}

// Check if the current player wins the game
function checkWin() {
    var theWinningPattern = -1;
    var playerPattern;
    if (crossPlaying) {
        playerPattern = crossPattern;
    } else {
        playerPattern = noughtPattern;
    }

    // Check if playerPattern is one of the winning patterns
    for (var i = 0; i < WINNING_PATTERNS.length; i++) {
        if ((WINNING_PATTERNS[i] & playerPattern) === WINNING_PATTERNS[i]) {
            theWinningPattern = WINNING_PATTERNS[i];
            break;
        }
    }

    // Change the class name of the cells of the winning pattern
    // CSS class-selector displays them differently
    if (theWinningPattern > -1) {
        for (var cellNum = 0; cellNum < NUM_CELLS; cellNum++) {
            var elm = document.getElementById("cell" + cellNum);
            if (theWinningPattern & Math.pow(2, cellNum)) {
                elm.className = "winningCell";
            }
            elm.onmousedown = null; // disable mouse click for all cells
        }
        return true;
    } else {
        return false;
    }
}