UPDATED TO SWIFT 5
We can get pretty descriptions of type names using the instance variable through the String initializer and create new objects of a certain class  
Like, for example print(String(describing: type(of: object))). Where object can be an instance variable like array, a dictionary, an Int, a NSDate, etc.
Because NSObject is the root class of most Objective-C class hierarchies, you could try to make an extension for NSObject to get the class name of every subclass of NSObject. Like this:
extension NSObject {
    var theClassName: String {
        return NSStringFromClass(type(of: self))
    }
}
Or you could make a static funcion whose parameter is of type Any (The protocol to which all types implicitly conform) and returns the class name as String. Like this:
class Utility{
    class func classNameAsString(_ obj: Any) -> String {
        //prints more readable results for dictionaries, arrays, Int, etc
        return String(describing: type(of: obj))
    }
} 
Now you can do something like this:
class ClassOne : UIViewController{ /* some code here */ }
class ClassTwo : ClassOne{ /* some code here */ }
class ViewController: UIViewController {
    override func viewDidLoad() {
        super.viewDidLoad()
        // Get the class name as String
        let dictionary: [String: CGFloat] = [:]
        let array: [Int] = []
        let int = 9
        let numFloat: CGFloat = 3.0
        let numDouble: Double = 1.0
        let classOne = ClassOne()
        let classTwo: ClassTwo? = ClassTwo()
        let now = NSDate()
        let lbl = UILabel()
        print("dictionary: [String: CGFloat] = [:] -> \(Utility.classNameAsString(dictionary))")
        print("array: [Int] = [] -> \(Utility.classNameAsString(array))")
        print("int = 9 -> \(Utility.classNameAsString(int))")
        print("numFloat: CGFloat = 3.0 -> \(Utility.classNameAsString(numFloat))")
        print("numDouble: Double = 1.0 -> \(Utility.classNameAsString(numDouble))")
        print("classOne = ClassOne() -> \((ClassOne).self)") //we use the Extension
        if classTwo != nil {
            print("classTwo: ClassTwo? = ClassTwo() -> \(Utility.classNameAsString(classTwo!))") //now we can use a Forced-Value Expression and unwrap the value
        }
        print("now = Date() -> \(Utility.classNameAsString(now))")
        print("lbl = UILabel() -> \(String(describing: type(of: lbl)))") // we use the String initializer directly
    }
}
Also, once we can get the class name as String, we can instantiate new objects of that class:
// Instantiate a class from a String
print("\nInstantiate a class from a String")
let aClassName = classOne.theClassName
let aClassType = NSClassFromString(aClassName) as! NSObject.Type
let instance = aClassType.init() // we create a new object
print(String(cString: class_getName(type(of: instance))))
print(instance.self is ClassOne)
Maybe this helps someone out there!.