I had a great time at JavaOne this year and Red Hat had a fantastic showing, with many sessions at the event, many more booth sessions (which were packed out as usual) and of course I made a brief appearance during the kickoff keynote. There had been a lot of interest in this event due to some recent events and rumours about what Oracle would or wouldn't say, specifically about the future of Java EE. This was even a topic of conversation during the JCP EC face-to-face meeting preceding JavaOne. But nothing much really happened and life, it seemed, would go on as usual. However, there was still a lot of discussion during several sessions and through the usual chatter on the floors or parties about the relevancy of Java EE these days.
But let's face it, this isn't a question that is only being asked in 2015; I've been involved in enterprise Java since before it was called J2EE and within a few years of bring created people were asking the same question. As I've mentioned many times over the past few years, people have asked the question when Web Services came along, then REST, PaaS/Cloud, mobile and now IoT. Each time the concept of middleware has evolved and Java EE, and its associated implementations, with it. People get hung up on the concept of Java EE and application servers as bloated, monolithic entities without actually looking at the reality of today's implementations (well, at least one). However, I'm not here to repeat what I've said time and time again (remember this from 2011?), most recently at HPTS 2015. Approaches such as WildFly Swarm and the massive interest it has seen, show that there's still a lot of interest. And I've already suggested how Java EE can fit into the next generation platforms.
Rather than revisit this question, which I think I've answered sufficiently, I wanted to link to Ian's entry on the JavaOne session he did, which I attended. It's always good to hear from someone else on the topic, though I'm sure some will argue he's not objective about this and neither am I. If you're still not convinced, think of the core capabilities within any Java EE application server, such as transactions, messaging, security, cacheing etc; services/capabilities that are needed way beyond Java and Java EE, pre-dating Java by decades and used together or independently in many applications. You can consider Java EE as a way of packaging these things together into a convenient bundle, where they are guaranteed to work well together or independently, and in most cases you probably don't even know they're there. Over the years, before Java was created and way beyond when it is just a mention in history books, that packaging will change but you'll still have something recognisable within middleware implementations, perhaps not co-locating services, perhaps not all implemented in the same language etc. And your future applications will probably not be able to tell the difference or know they're there ... again.
So whilst I think the original question is an important one to ask, I think a much better question is "Where should I use the core capabilities within Java EE?" And if you've got a suitably flexible and agile application server implementation, your application won't need to care that Java EE is, or is not, under the covers providing the desired dependability and reliability.