09/15/2008 Update: I wrote this article back in July, right after iPhone OS 2.0 was released. You’ll notice from the update on 08/01/2008 that I figured out what was going on. But since so many people keep asking, let’s establish something once and for all:

YOU CANNOT RUN APPSTORE APPS ON iPHONE 1.1.x!!!

It doesn’t work. It can’t work, since the 1.1.x version of the OS doesn’t support applications. You must install the 2.x version of the OS. 

Now, if you still want to read the original story, here it is:

OK, so I’ve got iPhone 2.0 loaded, and I successfully installed an app from the App Store from the device itself, but I can’t seem to get app installing working from within iTunes. I have downloaded three apps via iTunes and they all came down successfully, but they don’t show up on my iPhone. All three show up in the Applications pane of iTunes, so they successfully downloaded to my Mac, but even after manually syncing and unplugging and re-plugging the iPhone in, they never show up on the device. Going into the App Store on the iPhone itself and installing from there works, but I do get a message saying that I’ve already purchased that app, and would I like to re-download it for free. After that, the app is installed, but something is wrong. Or maybe I missed something.

08/01/2008 17:38 Update: I discovered the trick a day or so after I wrote this, but since someone else is still having the problem, I’m updating the post with the answer. Follow these steps

1. Click on your iPhone in the Devices section of iTunes
2. Click on the Applications tab
3. Check the “Sync applications” checkbox
4. Select either “All applications” or “Selected applications” and then check the ones you want synced.
5. Click the “Sync” button.

That’s it.