Short version: PCs will eventually eat consoles, graphics will become less important than story/game play, gaming will shortly emerge into a sort of golden age, and games will stand out more for its procedural and organic capabilities, which will allow it to be considered a serious and unique art.
The long version:
I think that the console/PC/Mobile gap is going to be around for a while, but will slowly disappear as stuff develops. Eventually your computer will connect to your TV via WiFi or cable, so there will be no reason to have a console to play games on. The only thing that will separate "console" and "PC" games will be whether you need a special controller or not, and most will probably use both. You won't need a Kinect, either, because you'll just use your Webcam.
As far as mobile devices go, like nenjin said, they'll continue to thrive on account of their portability, but I doubt they'll be able to reach the potential that a good PC can grasp (Both in terms of power and especially controls). Mobile gaming will probably still be 90% casual. There's also the possibility of playing mobile games on your home computer through a mobile device, but I don't see that as too common. Mobile gaming will become a force to be reckoned with, however, and will probably reach the point that PC gaming is at today, if it doesn't go further.
While graphics will definitely continue improving, we've already reached a point of realism that is desirable in a simulation. People actually like the way computer graphics make things less real by overextending certain elements, such as shadows and lightning effects, such as bloom, so that's probably around to stay. What we'll see in the graphics department is a greater focus on scale (IE, more bad guys, trees, blades of grass, etc), and a greater focus on style, game play, and story.
I see the video game industry as nearing a peak in the next few years. It's already kind of visible, but for a visualization I'll compare the video game industry to the film industry: Film started out as a hobby thing, moved on to making a quick buck, and then, as artists were able to express themselves fully in the new medium, began pumping out jewels and pieces that could be easily considered "art". I'm not saying that some pieces before this 'golden age' of film weren't art, but they didn't shake the medium like their predecessors. Since then, film has evolved into a science of genre and story telling.
Right now, we're approaching the point where artists have the ability, tools, and money to bring us into a golden age of video games. There'll be plenty of B-Games, disappointments, and cult classics, but the industry will develop in a way very unique to video games as an interactive medium, and have an impact because of this key difference in movies and other non-interactive mediums.
There will be plenty of games that stick to the linear design of story telling, but we'll see more and more games with highly interactive worlds and As AI and storytelling develops and becomes less linear, people will learn about the consequences of their actions in ways that occur completely naturally rather than by some designed action. You did X and Y happened, not because it was a scripted event in the story the game maker was telling, but because you did X.
Eventually we'll get to the point where game making is as much of an art as film making, and is treated as a serious form of expression. I tried to be vague with how long this will take, because access to information and technology is getting easier and easier, things can pick up really fast. That's a whole different topic, though.