Running iOS 6.1.3 through 6.1.6.

Use p0sixspwn. For 6.1.6, redsn0w too.

Running iOS 5.1.1.

Yep, just use redsn0w+absinthe2.

Running iOS 5.1.

iPhone 4S, iPad 2, and the new iPad: nothing.

Other devices: a tethered jailbreak is available.

You should bug the absinthe developers to support this iOS release.

Running iOS 4.2.9-10 or 4.3.4-5.

iPad 2: nothing.

Other devices: A tethered jailbreak is available.

You should bug the corona developers to support this iOS release.

Running iOS 4.2.6 through 4.2.8, or iOS 4.3 through 4.3.3.

Yep, you can use redsn0w.

(Or open JailbreakMe on the device itself.)