Note - when this question was asked in 2011 it was regarding the browser-based Minecraft Java Beta. As such it predates modern builds of Minecraft Java and Bedrock and support for Minecraft on other operating systems and platforms. The accepted answer was valid for the original intent of the question, but if you are encountering this problem today you may find better solutions in the other, more recent answers below.
Is there a way to alt-tab out of Minecraft (i.e. make Minecraft lose focus) without the game auto-pausing and without having to bring a menu (e.g. inventory) up first?