iOS: Google just released the iOS app for its Chrome-based remote desktop application. With the app installed on your iOS device and the extension in Google Chrome, you can login and use your home computer remotely.
Once you have the extension and the app installed, you can log in to your computer from your iOS device in a matter of seconds using your Google account. In a bit of brief testing, it works about as well as other remote desktop options, with the added benefit of being free.
Chrome Remote Desktop (Free) [iTunes App Store]