UPDATE July 2011: Thanks to reader Andrew for pointing out that Jailbreakme.com has been updated with a new jailbreak.
While jailbreaking the iPhone used to be a somewhat complex process that required solid technical skills, a website called JailbreakMe.com has taken advantage of a security hole in iOS 4 to make jailbreaking very simple.
It's important to know that Apple may close the security holes that JailbreakMe.com uses at any time. The process detailed in this tutorial works as of July 2011, but if you're reading it after that, Apple may have fixed the security hole. That said, Apple has fixed a number of holes and JailbreakMe.com has found new ones, so it's possible that new methods will appear even as old ones end.
Jailbreaking, of course, means that you'll be able to install non-Apple approved apps on your iOS device. You can do this via the Cydia app store, which is installed as part of JailbreakMe.com's process, or Installer.app/AppTap.
It's important to remember, of course, that by installing apps that you get anywhere other than Apple's App Store, you may be exposing yourself to malicious code or other trouble that Apple may not help you get out of.
To use JailbreakMe.com, you'll need an iPhone, iPod touch, or iPad running iOS 4.3.3 (to jailbreak iOS 3.2 or 4.0.1, try www.jailbreakme.com/star/. If you want to be able to jailbreak your device, don't upgrade beyond these OS versions.
To begin the jailbreaking process, point your device's browser to http://www.jailbreakme.com.