In honor of my sister receiving an iPad for her birthday today, I thought I'd do my own list.
Unless otherwise noted, all apps mentioned are free.
E-Mail and Calendar
Oddly, the built-in Calendar and E-mail apps don't do much for me. Since I share the iPad with my wife, I tend to use the web versions of Gmail and Google Calendar. I do have my e-mail credentials in the e-mail app so I can e-mail out pages from applications.
The #1 need here is to add Amazon's Kindle app. Amazon currently has more books available for Kindle then Apple does in the iBook store. More importantly, the Kindle is cross platform. You can only read iBooks on the iPad and iPhone. You can read Kindle on those and Android phones and many other platforms, including of course, the hardware Kindles Amazon sells.
Video and Television
In addition to the built-in Video and Youtube App, I also have Zap2It to give me TV listings, and IMDB to let me look up movies and actors. I also use Flixster to look up area movies; although I haven't been to one in ages.
The number #1 add on app in this area though is the Netflix app. With it, I can manage my queue, but more importantly watch streaming videos from Netflix. Their most basic membership of one DVD a month service lets you stream unlimited videos. You can start a video on your computer, pause it,m to watch it on on your TV via your Wii or PS3, pause it again, and resume on your iPad. In each case, the video starts up right where you left off.
I also have the AirVideoFree app. It lets me stream videos from my PC to my iPad. I'm still not sure I need it; I have it installed as an experiment. It works surprisingly well, and if I watched a lot of video I'd opt for the paid version. So far though I really don't see the need.
Also: ABC Player.
USA Today, AP News and NPR
WeatherBug and TWCMax (The Weather Channel)
The iPad was supposed to be a media consumption device, meaning web pages, books and videos. It's wonderful portability has made me want to use it for more productive things, and I've found a few apps that do wonderfully.
Evernote lets you build a collection of information. Most commonly they are notes but can also be audio notes, PDF files, photos, web clippings and bookmarks.
If you take a photo, Evernote can decipher the words in the photo so you can search on the words just as easily as you can words in a note.
For example if you take a photo of a historical marker of of the Manassas battlefield, when you search for Manassas, that image pops up along with all your other references to Manassas.
Evernote synchronizes the data in your client to their servers. If you run multiple clients as I do you have the same data on all platforms. There are free clients for iPad, iPhone, PC, Mac, Android and other platforms, as well as a web client.
I have a previous blog posts on the "Many Uses of Evernote" and "Your First Day with Evernote" that are worth checking out.
The beauty of Evernote, is you do not have to use iTunes to move information to your iPad.
Dropbox installs a small app on your PC that lets you move any file into a folder in "My Documents/My Dropbox" folder (on a PC) and it automatically syncs to their servers. Then if you have a free Dropbox client on another PC, a Mac, your iPad, or other platforms, the files are accessible there too.
The best use of this is for moving PDF files from your PC to be readable on your iPad.
To read PDF files, there are a number of good reader apps. I used GoodReader for a while (99 cents). It will open PDF files in Dropbox.
When my wife wanted to use the iPad at a professional conference, they e-mailed a bunch of PDF's and she wanted to annotate them. So we bought iAnnotate ($9.99). It stores its annotations right back into the PDF file so you can e-mail them back to yourself and read the annotations in Adobe's Reader application on your PC.
While iAnnotate does not open directly from Dropbox, it can download a PDF file from the web. I just go to the Dropbox website and open the file from there.
I can't imagine owning a platform without at least rudimentary word processing and spreadsheet abilities. More and more I have stopped using Microsoft Word and Excel in lieu of Google Docs apps. They may not have as many features as the Microsoft apps, but they have the features I use.
After looking at a variety of tools, I ended up with Docs2Go. It shares data with Google Docs It also is available on a large number of platforms If you haven't figured out, with Netflix, Kindle, Evernote, and Dropbox, cross platform flexibility is huge to me.
I love maps. I used to love waiting for the National Geographic to arrive with its map insert.
The built-in Maps app is great. I have also downloaded Google Earth, and ARCGIS.
There are many calculator apps out there. Many are 99 cents, but the "CalculatorXL" app is free and good enough for me.
Dictionary.com makes a nice dictionary.
QuickVoice will record audio.
Wikipanion is a nice way to access Wikipedia.
Photopad lets you edit photos, a sort of lite weight PhotoShop.
Siri I haven't used much, but probably would if I had a 3G iPad. You can ask with your voice to find all the Chinese restaurants nearby and it will. It's turns your iPad into sort of a computer as found on the Starship Enterprise. It is very cool. Apple just bought the company, so expect to see it as a built in app in the future.
And finally iDraft for drawing.
And while Skype does not yet have an iPad version, it does have an iPhone version that works ok on the iPad.
I have not bothered with iTunes links to each of the apps. Simple searches in the app store should let you find each of these apps.