Getting the coordinates from the location I touch the touchscreen

In a UIResponder subclass, such as UIView:

override func touchesBegan(touches: NSSet, withEvent event: UIEvent) {
    let touch = touches.anyObject()! as UITouch
    let location = touch.locationInView(self)
}

This will return a CGPoint in view coordinates.

Updated with Swift 3 syntax

override func touchesBegan(touches: NSSet, withEvent event: UIEvent) {
    let touch = touches.first!
    let location = touch.location(in: self)
}

Updated with Swift 4 syntax

override func touchesBegan(_ touches: Set<UITouch>, with event: UIEvent?) {
    let touch = touches.first!
    let location = touch.location(in: self.view)
}