iOS 7 seems to be laying the groundwork, but I can't wait 'til we push it just a tiny bit further... nothing unrealistic.
Notification Center does a pretty good job at showing me what I'm going to do today. But the lock screen is the gateway to me and my data, and it can do a lot better by taking some little steps.
A greeting. This humanizes the interaction between you and a technical device. My phone never leaves my side. Siri is my assistant. Someone finally discovered the "Happy Birthday" feature in the OS X setup. When I wake up, and first turn on my phone in the morning, there's no reason it can't greet me like an assistant or butler.
"Good morning. It's 62° and sunny."
The greeting can be switched out during the day of course to "Good evening," or have specific ones for different days. My phone is starting to learn where and when I go to work, it could even be used to nudge you. "Running late, today!" or even "Finally, the weekend."
Notification Center in iOS 7 tells me the weather for the day, but doesn't always give me the weather for now. The weather is so fascinating (and easy to collect data) that many apps are spawned to solve this. But all will pale in comparison if the lock screen ever shows it.
Meetings. Again, Notification Center has a kind of calendar view to show you your day at a glance, but it means again pulling it down from the lock screen or elsewhere in the system. At the very least, your soonest meeting could be displayed, and again, maybe with a nudge.
"You're meeting with Michelle in 23 minutes." or even "You only have 5 minutes to get to your meeting with Patrick."
Just as Music (while playing) takes over the lock screen, so too can this most basic information in the morning hours and even throughout your day.
I really hope to see these kinds of simple changes (and more!) happen in the future for iOS, because no app can solve these problems.