I've started using an iPad 2 for all Moodle/Work related business and here is a run down of my favourite 6 apps that are great for work.
Bamboo Paper
Price:
Free
Great handwritten note taking app, works great with a stylus or finger and has a choice of background paper styles
Evernote
Price:
Free
great for all sorts of notes/receipts and letters. A great way to manage your letters and notes
LogMeIn
Price:
Free
My favourite of all remote desktop apps, it works with its own desktop client rather than windows RDP.
Office2HD
Price :
£5.49
Great office app for the iPad. I love that this app also allows me to view and edit my Google Docs files on the go.
Dolphin Browser HD
Price:
Free
This App is a great substitute for Safari, has some nifty features like gestures and download, looks good too.
Penultimate
Price:
60p
A very powerful note taking app, like Bamboo works great with a stylus but this also allows users to annotate of images and photos.