在iOS 8和Swift 2.0中，请尝试这个，

override func tableView(tableView: UITableView, canEditRowAtIndexPath indexPath: NSIndexPath) -> Bool {
   // let the controller to know that able to edit tableView's row 
   return true
}

override func tableView(tableView: UITableView, commitEdittingStyle editingStyle UITableViewCellEditingStyle, forRowAtIndexPath indexPath: NSIndexPath)  {
   // if you want to apply with iOS 8 or earlier version you must add this function too. (just left in blank code)
}

override func tableView(tableView: UITableView, editActionsForRowAtIndexPath indexPath: NSIndexPath) -> [UITableViewRowAction]?  {
   // add the action button you want to show when swiping on tableView's cell , in this case add the delete button.
   let deleteAction = UITableViewRowAction(style: .Default, title: "Delete", handler: { (action , indexPath) -> Void in

   // Your delete code here.....
   .........
   .........
   })

   // You can set its properties like normal button
   deleteAction.backgroundColor = UIColor.redColor()

   return [deleteAction]
}

我知道这是一个老问题，但是@Kurbz的答案只需要Xcode 6.3.2和SDK 8.3

我需要添加[tableView beginUpdates]和[tableView endpdates](感谢@bay。phillips)

// Override to support editing the table view.
- (void)tableView:(UITableView *)tableView commitEditingStyle: (UITableViewCellEditingStyle)editingStyle forRowAtIndexPath:(NSIndexPath *)indexPath {
    // Open "Transaction"
    [tableView beginUpdates];

    if (editingStyle == UITableViewCellEditingStyleDelete) {
        // your code goes here
        //add code here for when you hit delete
        [tableView deleteRowsAtIndexPaths:@[indexPath] withRowAnimation:UITableViewRowAnimationFade];
     }

    // Close "Transaction"
    [tableView endUpdates];
}

在启动期间(-viewDidLoad或在storyboard)做:

self.tableView.allowsMultipleSelectionDuringEditing = false

重写以支持表视图的条件编辑。只有当你要为某些项返回NO时，才需要执行这个操作。默认情况下，所有项目都是可编辑的。

- (BOOL)tableView:(UITableView *)tableView canEditRowAtIndexPath:(NSIndexPath *)indexPath {
    // Return YES if you want the specified item to be editable.
    return YES;
}

// Override to support editing the table view.
- (void)tableView:(UITableView *)tableView commitEditingStyle:(UITableViewCellEditingStyle)editingStyle forRowAtIndexPath:(NSIndexPath *)indexPath {
    if (editingStyle == UITableViewCellEditingStyleDelete) {
        //add code here for when you hit delete
    }    
}

对于Swift，只需要写这段代码

func tableView(tableView: UITableView, commitEditingStyle editingStyle: UITableViewCellEditingStyle, forRowAtIndexPath indexPath: NSIndexPath) {
        if editingStyle == .Delete {
            print("Delete Hit")
        }
}

对于Objective C，只需编写以下代码

- (void)tableView:(UITableView *)tableView commitEditingStyle:(UITableViewCellEditingStyle)editingStyle forRowAtIndexPath:(NSIndexPath *)indexPath {
       if (editingStyle == UITableViewCellEditingStyleDelete) {           
            NSLog(@"index: %@",indexPath.row);
           }
}

同样，这也可以通过以下方法在SWIFT中实现

func tableView(tableView: UITableView, commitEditingStyle editingStyle: UITableViewCellEditingStyle, forRowAtIndexPath indexPath: NSIndexPath) {
    if (editingStyle == UITableViewCellEditingStyle.Delete){
        testArray.removeAtIndex(indexPath.row)
        goalsTableView.deleteRowsAtIndexPaths([indexPath], withRowAnimation: UITableViewRowAnimation.Automatic)
    }
}

SWIFT 5:适用于iOS 13+

func tableView(_ tableView: UITableView, canEditRowAt indexPath: IndexPath) -> Bool {
        return true
  }
    
    
 func tableView(_ tableView: UITableView, trailingSwipeActionsConfigurationForRowAt indexPath: IndexPath) -> UISwipeActionsConfiguration? {
        let deleteAction = UIContextualAction(style: .destructive, title: "Delete") {  (contextualAction, view, boolValue) in
            //Code I want to do here
        }
        
        let editAction = UIContextualAction(style: .destructive, title: "Edit") {  (contextualAction, view, boolValue) in
            //Code I want to do here
        }
        
        let swipeActions = UISwipeActionsConfiguration(actions: [deleteAction, editAction])
        
        return swipeActions
    }