ECActionSheetExample.m

// Example of a better API for UIActionSheet

- (void)showActionSheet {
  ECActionSheet *actionSheet = [[ECActionSheet alloc] initWithTitle:@"Title" cancelButtonTitle:@"Cancel"];

  // set a destructive button if needed
  [actionSheet addDestructiveButtonWithTitle:@"Destructive Button" target:self action:@selector(destructiveButtonPressed)];

  // add buttons with target/action
  [actionSheet addButtonWithTitle:@"Button One" target:self action:@selector(buttonOnePressed)];
  id someObject = something;
  [actionSheet addButtonWithTitle:@"Button Two" target:self action:@selector(buttonTwoPressed) withObject:someObject];

  // or add buttons with a block
  [actionSheet addButtonWithTitle:@"Button Three" onTapped:^{
    // do something when button three is tapped
  }];

  [actionSheet showInView:self.view];
}

- (void)destructiveButtonPressed {
  // do something when destructive button is tapped
}

- (void)buttonOnePressed {
  // do something when button one is tapped
}

- (void)buttonTwoPressed:(id)someObject {
  // do something with someObject when button two is tapped
}

UIActionSheetExample.m

// Example of an equivalent UIActionSheet API

@property (nonatomic, strong) id someObject;

- (void)showActionSheet {
  self.someObject = something; // set property to access it later
  UIActionSheet *actionSheet = [[UIActionSheet alloc] initWithTitle:@"Title" delegate:self cancelButtonTitle:@"Cancel" destructiveButtonTitle:@"Destructive Button" otherButtonTitles:@"Button One", @"Button Two", @"Button Three", nil];
  [actionSheet showInView:self.view];
}

- (void)actionSheet:(UIActionSheet *)actionSheet clickedButtonAtIndex:(NSInteger)buttonIndex {
  NSString *clickedButtonTitle = [actionSheet buttonTitleAtIndex:buttonIndex];

  if ([clickedButtonTitle isEqualToString:@"Destructive Button"]) {
    // do something when destructive button is tapped
  } else if ([clickedButtonTitle isEqualToString:@"Button One"]) {
    // do something when button one is tapped
  } else if ([clickedButtonTitle isEqualToString:@"Button Two"]) {
    // do something with self.someObject when button two is tapped
  } else if ([clickedButtonTitle isEqualToString:@"Button Three"]) {
    // do something when button three is tapped
  }
}

It would be nice if the UIActionSheet constructor initWithTitle:delegate:cancelButtonTitle:destructiveButtonTitle:otherButtonTitles: was still supported so that it could be a drop in replacement.

This could just be a simple subclass with additional features.

I think this is straightforward enough using this:
https://gist.github.com/4353703

- (void)presentCameraOrPhotoLibraryActionSheet
  {
    UIActionSheet *actionSheet = [[UIActionSheet alloc] initWithTitle:@"CameraOrPhotoLibrary"
                                                             delegate:self
                                                    cancelButtonTitle:@"Cancel"
                                               destructiveButtonTitle:nil
                                                    otherButtonTitles:@"Take photo or video...", @"Choose from library...", nil];

    [actionSheet showInView:[self tableView]];
}

- (void)actionSheetActionCameraOrPhotoLibrary:(UIActionSheet *)actionSheet clickedButtonWithTitle:(NSString *)buttonTitle
{
    UIImagePickerController *imagePicker;

    if ([buttonTitle isEqualToString:@"Take photo or video..."]) {
        imagePicker = [TCMediaPicker imagePickerForCamera];
    } else if ([buttonTitle isEqualToString:@"Choose from library..."]){
        imagePicker = [TCMediaPicker imagePickerForPhotoGallery];
    }

    [imagePicker setDelegate:self];
    [self presentViewController:imagePicker animated:YES completion:nil];
}

I see. I'm trying to solve the problem of the long if..else if... block in a single method. Also, I want to make it easier to pass an object to a button's action without having to store it in a local property.

Your solution solves the multiple action sheet per controller with a naming convention. My app needs a little bit more.