System Requirements for Unity development

Windows: XP SP2 or later; Mac OS X: Intel CPU Leopard 10.6 or later. Note that Unity was not tested on server versions of Windows and OS X.
Graphics card with DirectX 9 level (shader model 2.0) capabilities.  Any card made since 2004 should work.
Using Occlusion Culling requires GPU with Occlusion Query support (some Intel GPUs do not support that).

System Requirements for Unity iOS development
In addition to the general system requirements:

Only Unity OS X version supports iOS as build platform
Xcode 4.x

System Requirements for Unity Android development
In addition to the general system requirements:

Android SDK and Java Development Kit (JDK)
Android authored content requires devices equipped with:
Android OS 2.0 or later
Device powered by an ARMv7 (Cortex family) CPU
GPU support for OpenGLES 2.0 is recommended

System Requirements for Unity-made Content

Windows XP or later; Mac OS X 10.5 or later.
Pretty much any 3D graphics card, depending on complexity.
Online games run on all browsers, including IE, Firefox, Safari, and Chrome, among others.