<div class="cell celldata cell_service_data" id="cell_service_rate_1">
<input type="text" id="rate_service_row_1" class="rate_service_row"/>
</div>
<div class="cell celldata cell_service_data" id="cell_service_rate_2">
    <input type="text" id="rate_service_row_2" class="rate_service_row"/>
</div>

$('.rate_service_row').keydown(function (e) {
    var rateId = $(this).attr('id');

  var keyCode = e.keyCode || e.which,
      arrow = {left: 37, up: 38, right: 39, down: 40 };

  switch (keyCode) {
    case arrow.left:
      //..
    break;
    case arrow.up:
      //..
    break;
    case arrow.right:
      //..
    break;
    case arrow.down:
         //Set focus to the same cell next row
    break;
  }
});

var rateId = $(this).attr('id');
//Get the number of the currently selected cell
var curCell = rateId.substr(-1);

... code ...
case arrow.down:
     //Go one row lower.. so plus 1
     var newCell = curCell + 1;
     //Define the new identifier
     var newCellId = 'rate_service_row_' + newCell;
     var element = $(newCellId);
     //Focus on the element if it exists (element.length checks that)
     if (element.length != 0) {
          element.focus();
     }
break;