Wow, reading the title of this just made me realize that most implementations of "push" web content are actually browsers asking a server for content that doesn't exist yet. I guess that's what comes after the real-time web: content from the future! :)
The predictive semantic web, clearly. Type a few words, like "cat food obese" and it'll order you a bag of healthy cat food, a treadmill, and, six months later, a small wooden box and a new cat.