Thanks to pod2g and all his hard work, an untethered jailbreak is now available for the original iPad, iPhone 4, iPod touch 4, and older models. Both redsn0w and Corona have been updated to support the new, untethered jailbreak.
A few days ago, @pod2g gave the untether to both the iPhone devteam and the chronic devteam. We've put it into redsn0w 0.9.10 and PwnageTool, and the chronic devteam put it into a Cydia package (the same set of exploits is in all three).
Unfortunately, Apple A5 chipset-powered devices, namely iPhone 4S and iPad 2, are still in jailbreak limbo.
Because those devices cannot use geohot's limera1n exploit to inject the untether, they require exploits above and beyond those used for this release. Keep following pod2g on twitter or his blog for any progress reports!
Hit the source links below to start jailbreaking iOS 5.0.1 untethered, and if you need any help jump on into our jailbreak forums.