2020... not much will change, really.
There will still be DSLR's. Some may have hybrid viewfinders, some might not really be an "SLR" and might be EVF with no mirror. Whatever, the current form factor for a DSLR *WORKS* for a larger camera with larger cameras, and will still be around. :P DSLRs will come with wifi...and perhaps even cell contract options. Can you see greedy Canon selling a discounted Rebel with a monthly fee for two years at Verizon? Yeah. I can, too.
The EF and F and whatnot mounts will still be around. I wouldn't be surprised if there are less APS-C models as some of the lower end market gets won over by mirrorless--but I bet you anything there will still be some. HOWEVER, if you want to be real pedantic about terms used, I bet that those APS-C options will be mirrorless F and EF mount cameras with an EVF, in an slr-like form factor.
There will still be smaller sensors. There will still be point and shoots. However, point and shoot cameras will be more like cell phones in that there will be connectivity (wifi, etc, perhaps some prepaid no-contract options, too). There will be more camera-focused cell phone options. I wouldn't be surprised if at least one camera manufacturer merges with a consumer electronics giant.
Mirrorless cameras will have more market share--I bet at least one of the current player's offerings will be gone. My guesses for being gone would be Fuji. I predict micro 4/3 will be the dominant player, with Sony or Canon as number 2. Samsung will still be around but will be uncommon, but will be cult hits because they will have awesome lenses (odd prediction I know, but it's already started to happen).
All in all, not a ton will have changed. FF sensors will NOT become super cheap. Moore's law does not apply here. In fact, it's the opposite. They cannot shrink in size, thus they stay expensive or even get more expensive to make as they get built on more and more advanced processes. For a given size of chip, if you go to say TSMC and get a chip made, the more advanced the process, the more it costs. However, until the most recent 28nm process supposedly, the size reduction you'd get from the new process would save you money, so you went with it. Fortunately, FF sensors won't require a super advanced process unless we start getting 500mp or 1gp sensors!
FF cameras will get cheaper, though--a camera made without the mirror, with an electronic shutter, without the precision glass of an optical viewfinder, etc...that cuts costs immensely.
We'll get maybe one more real stop of high iso performance. The rest will be noise reduction or very clever processing.
We'll still be using Bayer sensors. Except for Sigma, I suppose? =p Just a hunch.
Canon will catch up in Dynamic Range, but Sony will remain the top sensor tech house due to insane volume (from cell phones). The world is already seeing that other companies can use column based amps and digital CDS, not just Sony. Canon might even catch up while still using off chip ADCs. =p We'll see.