One of the recurring themes regarding the iPhone at the Daring Fireball talk was the open question as to wether-or-not the iPhone will support 3rd party applications. Obviously, nobody outside of Apple knows the answer to this question yet (and my guess is that Apple itself hasn't decided yet), but I do feel the need to speculate.
The first thing that I noticed when I saw the "Home" screen on the iPhone was how it looked crazy-similar to Dashboard in Mac OS X Tiger (10.4). The "Home" UI looks like a modified version of the widget picker in Dashboard. And later on in the talk, when Jobs showed the Weather and Stock widgets, it became glaringly obvious that the iPhone can run Dashboard widgets, probably unmodified.
And that makes perfect sense, if you think about it. What exactly is a Dashboard widget? Well, it is a bundle of HTML, CSS, images, and Javascript, that is all rendered using Safari. And during the keynote, Steve made sure to mention explicitly that the iPhone runs Safari. So, it's not much of a stretch to think that the iPhone can run Dashboard widgets. So, I think that it's pretty likely that developers we'll be able to install 3rd party Dashboard widgets on our iPhones, when we get them in June.
And of course, it almost goes without saying (but I'm sure people will forget if I don't say it), that the iPhone will be able to run web applications. Those web applications that work in Safari today will probably work on the iPhone as well. But if the iPhone becomes a success (and I think that it certainly will), then we might start seeing a whole new breed of web applications that are written with the iPhone in mind.
But developers are going want close ties into the system, to write applications that cannot be expressed using JavaScript. And since the iPhone runs a slimmed down version of "OS X" (as Apple is referring to the operating system running on the iPhone), then all Mac developers should already have the tools that they need in order to write native applications for the iPhone. Wether-or-not Apple is going to allow this, however, is hard to predict.
A "computer", in the traditional sense of the word, is expected to be able to run any sort of 3rd party software. However the iPhone, as billed by Apple, is not a computer. So, I can see Apple take the closed approach with this thing. In general, this would jive with how games have worked on the iPod (totally closed), and how companies like Cingular like to run their CPE devices (you get applications and things for your device from Cingular, not from the Internet).
On the other hand, Apple is competing with devices that run Palm OS, Windows Mobile, and Symbian OS - all of which support 3rd party applications.
So, in the end, this one is really a toss up. My bet is that Apple will try to make the iPhone a closed platform. But since the iPhone appears to be such a kick-ass platform, I also predict that it won't be long before the hacking community is running homebrew application on their iPhones. :)
-Andy.
Update: Looks like TUAW has some quasi-confirmation that the iPhone won't run 3rd party applications.
Update 2: More reasoning from Steve Jobs as to why the iPhone won't support 3rd party applications.