I have an Apple iPad for a couple of months now and here are some of the apps i can recommend:
Best document viewer ever. Fast as hell and worth any money.
Sometimes I need to remotely login to a Windows maschine, and here comes RDP. There is a free version of the app available which lacks a couple of features. If you need those (like drag & drop) you need to get the paid version. Very useful!
This app helps you keep an updated DVD / BluRay collection. You can use the camera of the pad as barcode reader and instantly add your volumes. There is also a functionality to take notes when you lend your DVD’s to someone, so you always know, where your stuff is! Sometimes it crashes, but hopefully that will be addressed by the devs.
Note Taker HD
Take some notes anytime you want.
Since the iPad has no SD slot, you can use Dropbox to transfer all kind of data to your iPad.
Flipboard is a news reader which arranges the news in a newspaper style. It can follow your Facebook and Twitter accounts and compile a sort of newspaper for you, including information behind links.
Very good and innovative program!
Windowshop from Amazon
Amazon shopping easy and comfortable.
RSS Reader, especially useful in combination with a Google Reader account.
I haven’t tried out the paid version, but the free version offers a lot of stuff already. If you have a computer with TeamViewer installed, you can remotely access it with this app.
If you are new in town and need to find a certain locality (e.g. restaurant) this is your way to find it. This free app from one of the top directory and local search companies in Germany comes free of charge and is really useful in situations where you don’t know a phone number or address of the place you wanna go to. Germany only!
Watch and bid on auctions. Very easy to use.
Finally there is a Skype app for iPad which is really good and a real alternative to Facetime which can only be used with Apple devises.