Hopefully there will less screen-tearing and less FPS drops.

Consider the fact that the XBOX360 and PS3 made a massive leap in graphical capabilities.  And lately, Sony and MS have been trying to emphasize that they will wait until 2014 or later to make a new console.  And there's the compelling evidence that both MS and Sony are heavily switching to a casual focus, lending to the idea that future consoles will try to be cheaper in order to capture a larger portion of the market (like the PS2 and Wii did).

Considering all of this, its probably fair to say MS and Sony are looking to wait until a later date when increased technology can make a system cheaper and stronger at the same time.  In short, they're waiting until they can make a $300 system that is more powerful than XBOX360 or PS3.  But even with the nearly 8 years planned for the 'next gen' for Sony and MS, I highly doubt it'll be as massive an upgrade as this gen.

It may just be the edge Nintendo needs.  If they come out with a system equal or slightly more powerful than the current 360/PS3 and it comes out before the next Sony and MS offerings, it could really take over.

...or third parties will just completely ignore it like the Wii again.

the reason third parties ignored it was because they would basically have to make two seperate games, one for the hd consoles and one for the wii. If the rumors are true, that is why the next wii will be similar to ps3 and 360. Third parties will be able to pretty easily port their games to all three consoles.

Hopefully that will be the case.  And hopefully any new Nintendo system will actually be even stronger than the current 360/PS3, if only by a little.

I also think, even if a next gen console was twice the power of the current consoles, people probably wouldn't notice such a leap.  Just more polygons and crisper graphics, but no major leaps.  But that goes into my views of the uncanney valley and how developers need to focus on things like character animation and computer AI over sharper graphics to make the 'next' leap in graphics.

They will probably get closer to CGI like graphics with the next gen

I would like to see more native 1920x1080 games (I think we have 2 now, wipeout hd and ridge racer 7).

It is 2.25x the number of pixels of 1280x720 which was 2.25x of 854x480, just as big a jump as this gen, ie if you have a 1080p tv of big enough size to see the difference.

The first games of the new gen won't be very impressive. They'll run better but they'll look pretty similar at first. Just as Kameo, Dead rising, Resistance 1, etc. Higher res, more things on screen, but still looking very much like last gen. It will probably look disappointing at first from you tube videos and low res screenshots.

What I hope to never see again is screen tearing, sub 30 fps, sub 720p, excessive pop in, low res textures and long loading/install times. Fix that first then go higher res or more fancy effects.

It absolutely will.

The time between last gen and this gen was 5.5 years (the PS2 kicked off last gen in March 2000 and the X360 in Nov 2005)

This time around the difference will most likely be a whole 8 years between generations (from X360 in Nov 2005 to the Xbox 3 in Nov 2013). Even if next gen consoles might be designed slightly less powerful relatively speaking, those extra 2.5 years of improved graphics tech will make up for that and then some more, and ensure that the jump will be huge. At minimum it will be a 16 times increase in raw computing power from the X360 to the Xbox 3.

In late 2013 the most powerful PC GPUs on the market will be Radeon 9970s and Geforce GTX 880s, which will probably be at least twice as fast as the fastest single-GPU card today, the GTX580, and next gen console GPUs will be loosely based on those.

I doubt the jump will be as noticeable as in previous generations. There is a point where much improvement is impossible. We're not there yet, but I think advancements in the graphics department will slow down.

So do you think the PC graphics jump from Crysis to now has been as large as that from 2000-Crysis?

if you look at the graphics of every game other than crysis thenj the jump since 2000 to now has been unbelivable. You have to remember that there is still no single-gpu graphics cards that can max crysis at 60fps. Crysis was waaaaaaaaay ahead of its time.