UPDATE Swift 5.x
// duration will helps to control rotation speed
 private func rotateView(targetView: UIView, duration: Double = 5) {
    UIView.animate(withDuration: duration, delay: 0.0, options: .curveLinear, animations: {
        targetView.transform = targetView.transform.rotated(by: .pi)
    }) { finished in
        self.rotateView(targetView: targetView, duration: duration)
    }
}
Swift 2.x way to rotate UIView indefinitely, compiled from earlier answers:
// Rotate <targetView> indefinitely
private func rotateView(targetView: UIView, duration: Double = 1.0) {
    UIView.animateWithDuration(duration, delay: 0.0, options: .CurveLinear, animations: {
        targetView.transform = CGAffineTransformRotate(targetView.transform, CGFloat(M_PI))
    }) { finished in
        self.rotateView(targetView, duration: duration)
    }
}
UPDATE Swift 3.x
// Rotate <targetView> indefinitely
private func rotateView(targetView: UIView, duration: Double = 1.0) {
    UIView.animate(withDuration: duration, delay: 0.0, options: .curveLinear, animations: {
        targetView.transform = targetView.transform.rotated(by: CGFloat(M_PI))
    }) { finished in
        self.rotateView(targetView: targetView, duration: duration)
    }
}