For casual viewing of webpages the thing is unmatched. Its also pretty rad for ebooks, Netflix, and other ultra-casual "consumptive" internet behaviors like Facebook or just cruising through Flicker or eBay.
If you are into astronomy, there is SkySafari, which I used to help me track the most recent lunar eclipse. The interface is a bit smoother than what I use on my Mac (TheSkyX).
Another thing I like are those apps devoted to specify radio shows or webpages. The IMDB one is nice. The one for This American Life is pretty rad (if you like that show) because it also doubles as a donation to the show. It only costs a few dollars and you get all the TAL stuff organized in one place with a load of bonus junk too.
Now, all of this stuff can be done on an iPhone as well, but here's something that works much better on the larger screen: Virtuoso Piano.

At first glance it looks like a pretty no frills piano emulator, and it is, but what is totally cool is that you can chose which part of the keyboard those rows represent, and you can flip them to make it a versus dueling pianos thing, which is really fun if two people know how to play. You can probably do that on the iPhone/Touch version, but it would be much harder.
All of this stuff is, as I said, a distraction. I can do it all better with other hardware. If you add a keyboard all you have is a shitty laptop. Apple stuff is best enjoyed the way it is. If you fight the design, you just end up pissed off at it. If you have a lot of typing to do you should be using a real computer, not carrying around some stupid thing that triples the size of the iPad. Another thing to avoid: "free" apps. The ones that shove so many f*cking adds in your face you might as well have bought a Toshiba netbook for half the price.
All of this cool stuff makes me hope that the huge success of the iPad brings me the product I've wanted for ages, a touch screen MacBook. Basically what I have already (a real CPU, OS, keyboard, etc at real resolution) but with a bendy touch screen. That would be so f*cking rad, especially for music programs.