How to remove shadow behind popovers on iOS 9?

Swift 4 version of accepted answer.

override init(frame: CGRect) {
    super.init(frame: frame)    
    layer.shadowColor = UIColor.clear.cgColor
}

required init?(coder aDecoder: NSCoder) {
    fatalError("init(coder:) has not been implemented")
}

You can make your own custom popover background using UIPopoverBackgroundView

In the initWithFrame of your UIPopoverBackgroundView implementation, you can use a [UIColor clearColor for the drop shadow.

- (id)initWithFrame:(CGRect)frame
{
    self = [super initWithFrame:frame];
    if (self) {

        self.layer.shadowColor = [[UIColor clearColor] CGColor];
    }

    return self;
}