Great news for iPad 2 (or newer) owners! Pinnacle Studio (formerly known as Avid Studio) is currently available for $7.99USD.
Pinnacle Studio is a video editing app from Corel that arrived this past February, and was released to go head-to-head with Apple's own iMovie (also $4.99). It has been very well received and is definitely a worthy competitor.
Check out this video comparing the two video editing apps:
Even if you are just a casual videographer and have not tried editing the videos you take on your iPad, download it and give it a try when you have a few hours. Editing videos will only get easier over time. Use the videos you take with your iPad, or import higher-quality videos from other cameras using the camera connection kit, available for around $30USD.
Video transitions (the joining of two different clips) on Pinnacle are much better than iMovie, boasting 16 different ones that can make your videos stand out. iMovie on iPad to my knowledge only has the fade transition. Pinnacle Studio can export to 1080p high definition. Users can now export their creations to Box, YouTube, Facebook or email it to family and friends. Advanced users can export their files onto the PC version of Pinnacle Studio.
*Updated October 18, 2012:
Differences between Apple's iMovie and Pinnacle Studio
My colleague Matt of physedtech.org has worked extensively with both of these video editing apps. Here is a summary of the pros and cons of each:
iMovie:
Pros
Simple, powerful, clean, polished, tight integration with your iOS device (camera roll, copy and paste etc.)
Beautiful templates for trailers; easily create promotional videos for events, projects, etc.
Cons
Limited features, few choices for transitions, limited audio features, limited title effects and themes
Pinnacle Studio
Pros
Wealth of features: transitions, picture in picture video, motion titles, multiple audio tracks
Cons
Not as stable, occasionally crashes, rendering takes longer, libraries need to be updated frequently
Although it is no longer free, more advanced videographers will probably prefer all the features that Pinnacle have over iMovie. Check out this video highlighting it:
teachingwithipad.org 
It has no ability to download audio from the cloud. This program is useless. Pros should stay away. The audio recorder is really bad. And the only way to get more audio I’d from the music library. When editing or recording with other apps, there is no way to xfer the files into the library, with out a computer. Thus, it is not a mobile friendly app for people who work on the go. I mean that is why we got our pad to be mobile.
You make some good points. Pinnacle might be the best option out though. The audio limitations of iMovie are even larger. Let me know if you find anything better.