Currently, the iPhone and the iPad are not completely stand-alone devices. You can do a lot with them on their own, but there are just enough things that either require iTunes, or are better with iTunes, that keep them leashed to a desktop/laptop computer.
The one thing that still requires iTunes is upgrading the operating system. There isn’t a way to upgrade the OS on the iPhone or iPad without using iTunes to do it. Yes, the updates for them are generally very big, so doing an OS upgrade over the air using the 3G services is probably asking a bit much. But to do it over WiFi should be possible. This is one area, in particular, that keeps the iPad from being a truly one-for-one alternative to a netbook.
The other area is with media: right now, I have to plug my iPhone or iPad into a dock on my Macintosh to sync my media library. I can share libraries between computers with iTunes home sharing. It would be useful to be able to do that with the iPad, iPhone and iPod Touch as well.
Another place where independence doesn’t exist is with files: via iTunes, you can put files on your iPhone, iPad or iPod Touch for those applications that support them. However, it is on a per-application basis, and you now have multiple copies of the same file (one for each app and iOS device, plus whatever laptop/desktop you copied it from). For apps that support technologies like DropBox, you can use a cloud-based solution to share data between devices without requiring multiple copies. I would like to see it built-in on iOS devices. What I would like is a single copy of a file to exist (although each machine could keep a cached copy, and multiple parallel changes would need to be addressed) that I can access using multiple different applications. To be able to compose an e-mail and attach a document that is cached on the iPhone, or edit that same document on my iPad, or view it on my Mac, would be a powerful feature.
For me, it isn’t a big deal that I still need a desktop or laptop computer to manage my iPhone and iPad, and that data sharing is a bit clunky right now. But it would make some things easier if I could cut the cord, particularly the iPad. Being able to treat iOS devices as peers to MacOS, Windows, etc rather than subordinates, particularly for data, would make life easier. I use my iPad a lot like a netbook, and making a peer to the rest of my computing and storage would fit that model even more.