How to have stored properties in Swift, the same way I had on Objective-C?

As in Objective-C, you can’t add stored property to existing classes. If you’re extending an Objective-C class (UIView is definitely one), you can still use Associated Objects to emulate stored properties:

for Swift 1

import ObjectiveC

private var xoAssociationKey: UInt8 = 0

extension UIView {
    var xo: PFObject! {
        get {
            return objc_getAssociatedObject(self, &xoAssociationKey) as? PFObject
        }
        set(newValue) {
            objc_setAssociatedObject(self, &xoAssociationKey, newValue, objc_AssociationPolicy(OBJC_ASSOCIATION_RETAIN))
        }
    }
}

The association key is a pointer that should be the unique for each association. For that, we create a private global variable and use it’s memory address as the key with the & operator. See the Using Swift with Cocoa and Objective-C
on more details how pointers are handled in Swift.

UPDATED for Swift 2 and 3

import ObjectiveC

private var xoAssociationKey: UInt8 = 0

extension UIView {
    var xo: PFObject! {
        get {
            return objc_getAssociatedObject(self, &xoAssociationKey) as? PFObject
        }
        set(newValue) {
            objc_setAssociatedObject(self, &xoAssociationKey, newValue, objc_AssociationPolicy.OBJC_ASSOCIATION_RETAIN)
        }
    }
}

UPDATED for Swift 4

In Swift 4, it’s much more simple. The Holder struct will contain the private value that our computed property will expose to the world, giving the illusion of a stored property behaviour instead.

Source

extension UIViewController {
    struct Holder {
        static var _myComputedProperty:Bool = false
    }
    var myComputedProperty:Bool {
        get {
            return Holder._myComputedProperty
        }
        set(newValue) {
            Holder._myComputedProperty = newValue
        }
    }
}