Federico Viticci at MacStories put together an exhaustive list of features he'd like to see Apple include in iOS 7. I'm in agreement with most of them, but there are a few features that I'd really love to see.
Improved Notification Center. Notification Center is great, but I find it very annoying to have to manage every single notification that comes in. It would be awesome if Apple could somehow determine read status for things like iMessages and email, especially if I'm on another device. I don't want to see notifications for old emails and text messages that I've already seen. Also, I wish Apple would add a way to batch select and delete notifications. Having to manually go through each notification, tapping that minuscule 'X' button, is a major pain in the ass.
Cross-Device iMessage Reading. So many times, I'm working on my iPad with my iPhone next to me (like right now), and I'll get an iMessage on my iPad. I read it, but then the same message immediately chimes in on my iPhone. If Apple's server knows I saw a message on my iPad, then I shouldn't need to be notified on my other devices. I get sick and tired of hearing double chime sounds for the same message that I can already see on whatever device I'm using at the moment.
Set Default Apps. I've replaced many of the stock apps on iOS with better third-party alternatives from the App Store. Like many other nerds, I'd love it if Apple allowed users to define which apps are the default, as they do on OS X. Let me replace Calendar with Fantastical and Reminders with Checkmark. Relatedly, I'd love to see Siri's APIs go public so that I can ask her (it?) to play music from Rdio instead of the system Music app.