Some of the early commentary about the Apple iPad dismissed it as just a big iPhone or iPod Touch.
My iPhone sits in my pocket as I'm out and about, often in at least somewhat unfamiliar cities. I want to know which restaurants, which Wi-Fi hot spots, and which ATMs are nearby. I want to listen to music, glance at the news headlines, or play a quick, casual game. My iPad, by contrast, generally sits in my living room or accompanies me as a lightweight laptop substitute. I use it to read, take short notes, do e-mail, and entertain myself.
In other words, the differences in form factor tend to drive significant differences in the way I use the two devices.
My most useful iPhone applications tend toward those that can provide me with snippets of information and entertainment on the go, while the iPad is more about immersion for me--whether reading, watching video, or otherwise interacting.
Here are my favorite iPad apps:
Safari (free). The Safari Web browser is obviously an important part of the set of applications built into the iOS operating system for both the iPhone and iPad. However, I highlight it because the larger screen size of the iPad makes native Web browsing (lack of Flash support notwithstanding) much more natural than on the iPhone. Adding a bookmark to the home screen using Safari--a feature I'm embarrassed to admit I only belatedly discovered--is a great substitute for a native application in many cases.
iReeder for iPad ($4.99). If you're a heavy-duty consumer of blogs, Reeder makes it easy to skim through lots of them. Bookshelf ($4.99) seems more targeted at attractively presenting a more modest list. A decent free alternative is to just point Safari at Google Reader.
I read news on both my iPhone and iPad, though on my phone it's more about headlines and quick snippets than reading in-depth stories. My personal favorite on the iPad is probably The New York Times Editors' Choice (free), which is a worthy experiment in bringing a newspaper look and feel to a digital device. Other news applications that I favor are BBC News (free), Fluent News (free), and NPR (free).
Google Earth (free) comes into its own on an iPad. In the absence of a specialized controller for a PC, navigating around Google Earth is straightforward enough, but using a mouse with the program never felt particularly natural to me. The iPad's multitouch interface, by contrast, is a great match.
On the iPhone, Epicurious (free) makes for a handy recipe reference while pondering what's needed to cook up those great-looking veal chops in the meat aisle. In high definition on the iPad, Epicurious becomes a gorgeous digital cookbook. (I've also started to put other recipes I use online so I can pull them up on my iPad in the kitchen.)
The iPad has pros and cons as an e-book reader relative to devices such as Amazon.com's Kindle that use "electronic paper" displays such as E Ink. However, there is no real debate that the iPad is an e-book reader among other things. There are at least three good, free apps available for this purpose: Kindle, iBooks, and Stanza. Your favorite or most useful will depend on where you obtain your electronic books and on personal preferences.
In spite of its size, the capacitive screen technology used in the iPad means that it isn't as easy to write on as you might assume. A stylus, such as the Pogo from Ten One Design, that has a metal barrel and a tip made of a conductive foam commonly used to protect electronic components, helps. So does the right software. Dan Bricklin's Note Taker HD ($4.99) lets you write in a magnified window on the screen. I didn't find that this approach helped enough on the iPhone, but it works pretty well on the iPad. I can't draw to save my life. But for creating "napkin sketches" and other quick doodles, I like ArtStudio ($3.99).
Some of TweetDeck's (free) iPhone fans don't especially care for the different user interface it presents on the larger iPad. But I prefer it. I also find FlickStackr ($1.99) a particularly nice way to explore photographs on Flickr. Obviously, using the Web interface is an alternative to applications such as these, but I find that the separate app makes interacting easier.
I did say favorite apps, so I'd be remiss if I didn't close in mentioning Plants vs. Zombies HD ($9.99), an addictive game. I'm also eagerly awaiting the iPad version of Carcassonne. The popular tile-laying board game runs on the iPhone, but I can imagine it benefiting greatly from the iPad's increased screen real estate.