AirServer (available for Mac and Windows) allows you to do, without the need of having an Apple TV. Mirroring is supported by the iPad 2 or newer and the iPhone 4s or newer.
Whether it is showing off photos that are on your iPhone on to your computer screen or giving a presentation using AirServer on your notebook computer that is connected to a projector, or just playing one of the thousands iOS games on your computer screen, AirSever will enable all of this. On top of that you can connect multiple iOS devices to one display. There is a trial you can download which allows you to try it out for 7 days and if you decide to keep it, it's available for $15.