TeamViewer for Remote Control
The free TeamViewer for Remote Control app for iPhone is available for devices running iOS 4.3 and later, is optimized for the iPhone 5 and enables remote access to an unattended PC. The app makes it possible to control the mouse and keyboard, reboot the PC and adjust the screen resolution where required. You'll need the computer ID number and the personal password you created when you set up the desktop software in order to make a successful connection. Communications sent between TeamViewer apps are encrypted using 256-bit AES Session encoding and 1024-bit RSA Key Exchange standards.
LogMeIn
The LogMeIn client software is set up and configured through a desktop Web browser. Once this is done you can use the free LogMeIn app to get connected to your PC. You can open up files, launch applications, wake up a sleeping PC and perform any task you could if you were actually at your machine. For $39.99 a year as of August 2013 you can sign up to the Pro plan, which brings with it additional features such as HD video streaming and the ability to transfer files to your iPhone from the computer. The LogMeIn app is compatible with any device running iOS 4.3 or later and is optimized for the iPhone 5.
Splashtop Personal
Install Splashtop Personal on your iPhone, install the Streamer app on your computer, and you're ready to connect to your PC remotely. Splashtop Personal works with both PCs and Macs, runs on devices with iOS 5.0 or above and has been optimized for the iPhone 5. While the app is free to download, to access your computer over a Wi-Fi or 3G/4G connection you must purchase an Anywhere Access Pack from within the app. Prices start at $1.99 for a month's subscription as of August 2013. Splashtop Personal utilizes a fully secure, 256-bit AES encrypted SSL connection when in use.
Screens VNC
Screens VNC, available for $19.99 for the App Store as of August 2013, lets you control any computer remotely over the Web. It features iCloud integration to synchronize your stored screens across devices, a straightforward setup process, a secure SSH Tunnel connection and support for multi-touch input. The VNC acronym stands for Virtual Network Computing, a standard protocol used extensively for remote computer access but with some limitations such as an inability to transfer audio. The iPhone app requires iOS 5.1 or later to be running on your iPhone and is optimized for the iPhone 5.