The newly-released iPhone version of Skype works on the iPad -- sort of. Skype says the iPad still isn't officially supported, but will be covered in a future release.
Skype's announcement of the new iPhone version of Skype, including support for making calls across 3G networks (and which we covered earlier), wasn't terribly ambiguous about whether it worked on the iPad or not:
The new version is compatible with the iPhone, iPhone 3G, iPhone 3GS, iPod touch and iPad. Skype requires iPhone OS version 3.0 and above. Calling functionality is available on iPhone, iPhone 3G, iPhone 3GS and 2nd generation iPod touch onwards
That suggests that calling on an iPad isn't possible. However, a number of users (including the brother of Lifehacker's editor) reported that you could in fact make calls over Wi-Fi networks using the iPad. We asked Skype to clarify, and this is what we were told:
We have not yet released and announced an official iPad version of the Skype app. We have, however, released a quick update to our iPhone app which addresses a couple of iPad teething problems. You can download it now from the App Store, but please bear in mind that we are still tuning and testing the app to further improve the user experience for our customers. You can expect to hear more from us about an iPad app in the coming months.
If you've installed Skype on the iPad, tell us how it's working for you in the comments.