Will Java become the dominant platform for web applications? Actually, I think it has a good chance.
How will the future web applications be? I think we can expect the following:
* Highly interactive
* Complex, more work will be done on the client
* Collaborative, not only for games, but also for other applications
* Location aware
AJAX is fantastic compared to "web 1.0", and technology like GWT (Java) makes it relatively easy to develop complex user interfaces. But HTML and HTTP still sucks as an application platform, something they were never meant to be. I believe that if Microsoft hadn't managed to kill the Applet, Java would be the dominant platform for more complex web applications today.
I think Consumer JRE can be that platform. Java can be used to make complex, interactive applications that communicate with each other client-to-client.
This doesn't mean we have to implement in Java. When consumers have a JRE ready, there is nothing stopping us from developing applications in Groovy, JRuby and Scala and deliver them over the web.
I don't know much about Flash, but I am sure it is at least as good as Java for making flashy applications. But when it comes to complex collaborative and mobile applications, I think Java has the upper hand.
And Java has one more powerful force behind it: The community. The Java community has developed hundreds of libraries and frameworks. Too many, perhaps. But this community is capable of revolutionizing the way web applications are developed in ways we cannot predict now.