Push Notifications - save token id into a database using Asynchronous Request

First of all I think you could improve indenting (use Xcode built-in tool) and spaces.

Second thing you had 2 useless local variables.

And, most important, IMO you should create a struct or a class as your API client wrapper. Even if you have one simple method for now.

Here is a very simplified example.

func application(application: UIApplication, didRegisterForRemoteNotificationsWithDeviceToken deviceToken: NSData) {

    var userId = "001" //I just use it as USER number 1
    let token = deviceToken.hexString()

    let apiClient = MyRESTAPI(userId: "001")
    apiClient.setUserToken(token) {
        result in
        switch result {
        case .Ok(let response):
            println("data: \(response)")
        case .Error(let error):
            println("failed: \(error.localizedDescription)")
        }
    }
}


    struct MyRESTAPI {
        enum Result {
            case Error(NSError)
            case Ok(NSURLResponse)
        }

        let userId:String

        func setUserToken(token:String, completion:(Result -> Void)) {
            var postBody = NSString(format: "user=%@&token=%@", self.userId, token)
            var endBody = NSURL(string: "http://www.myServer.com/api/v1.0/register.php")
            var request = NSMutableURLRequest(URL: endBody!, cachePolicy: NSURLRequestCachePolicy.ReloadIgnoringLocalCacheData, timeoutInterval: 30.0)

            request.HTTPMethod = "POST";
            request.HTTPBody = postBody.dataUsingEncoding(NSUTF8StringEncoding)
            request.setValue("application/x-www-form-urlencoded", forHTTPHeaderField: "Content-Type")

            NSURLConnection.sendAsynchronousRequest(request, queue: NSOperationQueue.mainQueue()) {
                (response, data, error) -> Void in

                if data != nil {
                    completion(MyRESTAPI.Result.Ok(response))
                } else {
                    completion(MyRESTAPI.Result.Error(error))
                }
            }
        }
    }


    extension NSData {
        func hexString() -> String {
            // "Array" of all bytes:
            let bytes = UnsafeBufferPointer<UInt8>(start: UnsafePointer(self.bytes), count:self.length)
            // Array of hex strings, one for each byte:
            let hexBytes = map(bytes) { String(format: "%02hhx", $0) }
            // Concatenate all hex strings:
            return "".join(hexBytes)
        }
    }