Google Maps API Version difference

I’ve taken your request URL and pasted it in my app, which is using the newer version, and it works great.
The problem may be how you parse the data, or decode the received JSON string.

String url = "http://maps.googleapis.com/maps/api/directions/json?origin=19.5217608,-99.2615823&destination=19.531224,-99.248262&sensor=false";

HttpPost httppost = new HttpPost(url);
HttpResponse response = httpclient.execute(httppost);
HttpEntity entity = response.getEntity();
InputStream is = null;
is = entity.getContent();
BufferedReader reader = new BufferedReader(new InputStreamReader(is, "iso-8859-1"), 8);
StringBuilder sb = new StringBuilder();
sb.append(reader.readLine() + "\n");
String line = "0";
while ((line = reader.readLine()) != null) {
    sb.append(line + "\n");
}
is.close();
reader.close();
String result = sb.toString();
JSONObject jsonObject = new JSONObject(result);
JSONArray routeArray = jsonObject.getJSONArray("routes");
JSONObject routes = routeArray.getJSONObject(0);
JSONObject overviewPolylines = routes.getJSONObject("overview_polyline");
String encodedString = overviewPolylines.getString("points");
List<GeoPoint> pointToDraw = decodePoly(encodedString);

//Added line:
mapView.getOverlays().add(new RoutePathOverlay(pointToDraw));

and the decodePoly() method is taken from another question here in SO, which I don’t remember the author:

private List<GeoPoint> decodePoly(String encoded) {

    List<GeoPoint> poly = new ArrayList<GeoPoint>();
    int index = 0, len = encoded.length();
    int lat = 0, lng = 0;

    while (index < len) {
        int b, shift = 0, result = 0;
        do {
            b = encoded.charAt(index++) - 63;
            result |= (b & 0x1f) << shift;
            shift += 5;
        } while (b >= 0x20);
        int dlat = ((result & 1) != 0 ? ~(result >> 1) : (result >> 1));
        lat += dlat;

        shift = 0;
        result = 0;
        do {
            b = encoded.charAt(index++) - 63;
            result |= (b & 0x1f) << shift;
            shift += 5;
        } while (b >= 0x20);
        int dlng = ((result & 1) != 0 ? ~(result >> 1) : (result >> 1));
        lng += dlng;

        GeoPoint p = new GeoPoint((int) (((double) lat / 1E5) * 1E6), (int) (((double) lng / 1E5) * 1E6));
        poly.add(p);
    }

    return poly;
}

I’m including what I’ve used in order to add the overlay to the map itself as well,
I can’t find the tutorial it’s taken from.. sorry for not giving credit. (added the call to this in the first method I posted)

public class RoutePathOverlay extends Overlay {

    private int _pathColor;
    private final List<GeoPoint> _points;
    private boolean _drawStartEnd;

    public RoutePathOverlay(List<GeoPoint> points) {
            this(points, Color.RED, true);
    }

    public RoutePathOverlay(List<GeoPoint> points, int pathColor, boolean drawStartEnd) {
            _points = points;
            _pathColor = pathColor;
            _drawStartEnd = drawStartEnd;
    }


    private void drawOval(Canvas canvas, Paint paint, Point point) {
            Paint ovalPaint = new Paint(paint);
            ovalPaint.setStyle(Paint.Style.FILL_AND_STROKE);
            ovalPaint.setStrokeWidth(2);
            int _radius = 6;
            RectF oval = new RectF(point.x - _radius, point.y - _radius, point.x + _radius, point.y + _radius);
            canvas.drawOval(oval, ovalPaint);               
    }

    public boolean draw(Canvas canvas, MapView mapView, boolean shadow, long when) {
            Projection projection = mapView.getProjection();
            if (shadow == false && _points != null) {
                    Point startPoint = null, endPoint = null;
                    Path path = new Path();
                    //We are creating the path
                    for (int i = 0; i < _points.size(); i++) {
                            GeoPoint gPointA = _points.get(i);
                            Point pointA = new Point();
                            projection.toPixels(gPointA, pointA);
                            if (i == 0) { //This is the start point
                                    startPoint = pointA;
                                    path.moveTo(pointA.x, pointA.y);
                            } else {
                                    if (i == _points.size() - 1)//This is the end point
                                            endPoint = pointA;
                                    path.lineTo(pointA.x, pointA.y);
                            }
                    }

                    Paint paint = new Paint();
                    paint.setAntiAlias(true);
                    paint.setColor(_pathColor);
                    paint.setStyle(Paint.Style.STROKE);
                    paint.setStrokeWidth(5);
                    paint.setAlpha(90);
                    if (getDrawStartEnd()) {
                            if (startPoint != null) {
                                    drawOval(canvas, paint, startPoint);
                            }
                            if (endPoint != null) {
                                    drawOval(canvas, paint, endPoint);
                            }
                    }
                    if (!path.isEmpty())
                            canvas.drawPath(path, paint);
            }
            return super.draw(canvas, mapView, shadow, when);
    }

    public boolean getDrawStartEnd() {
            return _drawStartEnd;
    }

    public void setDrawStartEnd(boolean markStartEnd) {
            _drawStartEnd = markStartEnd;
    }
}

Hope this works for you.