This should work:
NSBundle.mainBundle().infoDictionary!["CFBundleName"] as! String
infoDictionary is declared as a var infoDictionary: [NSObject : AnyObject]! so you have to unwrap it, access it as a Swift dictionary (rather than use objectForKey), and, as the result is an AnyObject, cast it.
Update Swift 3 (Xcode 8 beta 2)
Always better to use constants (and optionals) where possible, too:
Bundle.main.infoDictionary?[kCFBundleNameKey as String] as? String