Remote desktop apps for the Mac and PC are reasonably common, and there are also an increasing number available for iOS. One of the most recent entrants to the arena is Splash Remote Desktop which can be used to take control of your Mac or PC using your iPhone or iPad, complete with full video and audio sharing.
As with all such apps you will need to install desktop software in order to be able to access your computer from your mobile device - this can be downloaded free of charge from the Splashtop web site. Once installed, there is virtually no configuration to worry about - just supply the password you are prompted to create during the installation process.
As things currently stand, Splashtop remote desktop can only be used with a wifi connection so this limits remote sessions to working with computers that are on the same network - a future update to the app will allow for remote sessions via 3G and easy connections when firewalls are involved.
A variety of finger gestures can be used to interact with your desktop computer and sound can be routed from your computer to your idevice. Thanks to the fact that you can view the contents of your desktop means that you can enjoy Flash video on your iPhone or iPad, or even play games.
The app can be used to control all versions of Windows from XP upwards, and there is a beta version of the desktop client available for OS X. As with all such tools, the iPad edition of the app benefits hugely from the additional screen real estate, but sterling work has been put into making the iPhone edition as useable as possible - it is just a shame that there isn't a free version available for the iPhone, although the free iPad edition only allows connection for up to five minutes.