3. Holodeck
Perhaps this is the greatest challenge set forward by Star Trek: The Next Generation. A room where interactive holograms can be created that use hard light (I'll go with the Red Dwarf terminology there) which you can touch, and not only that they feel real. There are so many steps before we can see this actually happen that even a sudden breakthrough in one field wouldn't lead to it. Before we see a holodeck, we have to create basic holograms as seen in the communications projects in Star Wars etc. We're getting there on that count. A combination of the sensors as seen in games consoles for game controller-less gameplay combined with a simple projection can result in a manipulable 2D "hologram". This isn't really the 3D version that we would expect, so that would be the next natural step. Once we have those, we'll have gone a fair way towards achieving a holodeck. But the problem will remain that it'll be "soft light" that is, your hands will be able to move through the hologram. So it'll simply make for an interesting way to watch television and perhaps something more similar to the controls as seen in the JJ Abrams Star Trek films. There would need to be some sort of way to have a projected manipulable gravity projection to prevent the user from moving through a hologram. Once all that is in place then a holodeck would be a possibility. Of course then you'd also need to have a programming language etc, but those are all child's play compared to the others. We already have those sorts of tools and by the time that the other technologies have been developed, the personal assistant devices that started with Apple's Siri should be sufficiently advanced to be able to understand what we want when we specifically ask for an original Sherlock Holmes story without a Moriarty who'll try to take over the ship.