Recommended

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Dropbox - Free
A great way to share files between devices. Place a file in the Dropbox and it is immediately available to every device connected to that Dropbox account - iPads, iPhones, computers and laptops (Mac or PC). School proxies caused an issue in earlier versions but Dropbox now has the ability to be set to your school's proxy setting. Many apps have built in support to save directly to Dropbox. Watch the YouTube video. Visit the Dropbox website.
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Jumbo Calculator - Free
Not much to say really - this is a larger button basic calculaor that flips to match the orientation of the iPad. It deserves a nod for being around since the beginning of the iPad and working simply and well.
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Lab Timer - Free
If you need a stop watch or recording facility this is a great app. The screen is divided into 4 large timers each of which toggles between 4 more timers - ie 16 independent timers, each of which can count up or down displaying hours, minutes and seconds. Customise the label for each timer to keep track of what is being recorded. The timer will continue to work in the background while using other apps - discovered a timer that had been left running and had dutifully kept counting for 6900 hours which was around 290 days.
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Skype - Free
Join up for a free Skype account and then video call or IM other Skype users anywhere in the world on any computer or mobile device. Talk face to face with front or back facing camera.

Worth Considering

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Keynote Remote - $0.99
Turn an iPhone,iPod touch into a remote control for your iPad or Mac when running a Keynote presentation. Operates over wifi or Bluetooth. Swipe to advance or return to another slide, view presenter notes and activate animations or videos. Simple to connect and effective to use. Presenting with Keynote remote YouTube video.
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OPlayer - $5.49
The standard video player on the iPad operates smoothly and does a nice job of playing iTunes related content, however it will only work with a limited number of file types. OPlayer adds versatility to the iPad by extending its video capability to include other common file types such as avi, wmv, mkv and many more less common file types. It also includes a range of advanced features such as FTP, streaming and dropbox support. YouTube video.
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Pimp Your Screen - $0.99
Eye candy for the iPad. Customise the iPad with a range of very high quality specially designed backgrounds that wrap perfectly around the icons on the screen. Selecting one is difficult because there are a large variety to choose from and the images are very well themed. YouTube video.
Prices are in $AUS and were correct at time of publication but are subject to change.