It goes without saying that not every CGI film attempts a more realistic style, but even the ones that don't usually try to look like something else. There's the faux-clayish preschool style, the silvery tech commercials/music videos/art films(I can't tell which is which), chinese ink, technological noir, crooked and rundown eyesores, and quite a couple of others.
With just about every approach now, the computer is used as a sandbox tool that largely mimics something else with a few concessions to computer physics. There isn't much of a computer look nowadays that stands out from the real world, and virtual reality has become virtually reality. There still are the rare films that look like they're made on a computer, but mostly from filmmakers who can't afford better rendering or who are aiming to break the mold somewhat self consciously. Earlier computer animators did their best to express their vision within quite restrained technology, and being blatantly computerized was inevitable for every approach.
Nowadays it seems like animation is going through a transitional period where computer animation is considered such a force in and of itself. The other important thing to keep in mind, though, is that even more traditional animators are using computers in their traditions. With computer drawn animation, flash, and computer use in stop motion, media forms are being divided every day. I think that computers are going to be incorporated more as a single essential tool of an overall technique. With the advances in robotics, I suspect that robotic animation will some day develop out of the traditions of stop motion, CGI and animatronics.
The 2D approaches to computer graphics are now effectively overwhelmed by old traditions, except for a few rebels taking inspiration from old video games. It's hardly even considered to be computer animation anymore to work in a 2D format on a computer, since the technology's become so good.
The progress of CGI to me is like a process where box that keeps getting carved into 8 smaller and smaller boxes of the same shape. First it isn't all that interesting because you can easily count the boxes, then it gets a little more interesting because there's enough to be interesting without being overwhelming, then it becomes impressive but unrelatable as there's many boxes to see but far too many to count. Eventually the boxes are microscopic in size, and you're still amazed when you can tell it's there. Finally, as the boxes get perpetually smaller, you work your way down to atoms and you're left with the same box you started with.