The iPad has recently been jailbroken. Even if you've held off jailbreaking your other iPhone OS devices, the iPad's substantially faster hardware and difficult-to-define "3rd device" role make the best case yet for jailbreaking. A user- and developer-updated compatibility list will help you see what's safe to install on your iPad, and I'll list my favorite apps and extensions for your freshly jailbroken device.
Apple's App Store has become notorious for its restrictive and often arbitrary decisions about what does and doesn't make it into the store. We've seen many pieces of quality software get denied or kicked out of the App Store, sometimes for unclear or unknown reasons.
Many of these, however, have subsequently made their way into Cydia, the jailbroken app installer (note that the App Store works just fine on jailbroken devices, too). GV Mobile, a great interface for Google Voice, Dashboard, a clone of Mac OS X's Dashboard for iPad, and Wifi Sync, a paid application for performing iTunes syncs over Wi-Fi, are just a few examples. And there are plenty more programs and extensions that are available in Cydia that have never even been submitted to the App Store.
Besides these examples of nixed software, the world of jailbreaking also offers a multitude of tweaks that aren't available to the user on a normal iDevice, like changing system sounds or interface elements. While a much higher proportion of the software available through Cydia is free compared to what you'll find on the App Store, it does also contain paid software.
The iPad: What’s Changed?
Many people express concern about jailbreaking their iPhones because they don't want to sacrifice stability or speed on their phones. While the vast majority of jailbreak software is perfectly stable, it's true that this software doesn't go through the same level of grueling testing to which Apple subjects software that makes it into the App Store. And software that lets you run 3rd-party programs in the background, otherwise change the interface, and so forth, can have effects on your device's performance, so I can understand why some people are reticent about this.
However, the iPad's processor and memory are substantially more powerful than that of the current iPhones and iPod Touches. Its hardware makes it much better suited to effective multitasking, and its role in most peoples' workflow makes a good for jailbreaking, both because jailbreaking makes it more useful, and because it simply won't be used the same way as your phone.