limera1n!

redsn0w is a utility that will jailbreak your iPhone or iPod Touch, allowing it to run apps that are not approved by Apple.

Greenpois0n performs an untethered jailbreak for iOS 4.2 on the iPhone 4/3GS, iPod touch 2G/3G/4G, iPad, and Apple TV 2, allowing them to run apps unapproved by Apple. It uses the limera1n exploit by geohot.

PwnageTool is an advanced jailbreaking application by the iPhone Dev Team for Mac OS X. It can build a pre-jailbroken .ipsw ("iPhone software") file with apps and anything else pre-loaded, so that you can run apps without the approval of Apple. PwnageTool can also hacktivate your phone, and lets you choose a custom boot logo.

Absinthe is a tool by the makers of greenpois0n that provides an untethered jailbreak on iOS 5.1.1, for the following devices:

(This is an OUTDATED jailbreaking method.)

sn0wbreeze is an advanced jailbreaking tool that lets you build a custom IPSW ("iPhone software") file. It allows you to jailbreak your iPod or iPhone, so that it can run apps unapproved by Apple. sn0wbreeze can also set up a custom boot logo, hacktivate your iPhone (if necessary), root partition size, and more.