Crop cameras hold their own in terms of image quality at low to medium ISOs. You have to pixel peep to see the difference these days, and the resolutions are generally comprable (Nikon D800 aside, of course). That may change, but greater resolution incurs a secondary cost in terms of processing power and storage space, which translates to loss of speed.
Crop cameras are at a depth of field disadvantage (full frame cameras can achieve a shallower depth of field), but that's primarily because most of the lenses available for them are shared with their full frame brethren. Lens manufacturers are beginning to address that issue somewhat (see, e.g., the Sigma 18-35 f/1.8), but I expect full frame to continue to win in that regard, particularly when one uses primes. Even so, one can achieve a decently shallow depth of field with crop equipment. But sometimes you need a super-shallow depth of field, or you need it with a relatively wide angle, and it is then that full frame comes into its own.
Where crop cameras come into their own is when you need "reach". Crop cameras put more pixels on target than full frame cameras, so as long as the lens is up to the task of resolving to the capabilities of the sensor, they're able to record more detail while making use of a relatively compact lens (there is absolutely no equivalent to the 55-250 IS in the full frame world -- anything that would achieve roughly the same angle of view range is much larger).
Because of their "reach", and because telephoto lenses are by far the most expensive out there, a crop setup can be significantly less expensive overall than an equivalent (with respect to angle of view range) full frame setup. Generally speaking, once you hit a certain (rather long) focal length, a sufficiently shallow depth of field is no longer really an issue, so reach itself then becomes the thing that matters.
For the above reasons, I don't think crop cameras are going anywhere. There's a significant market for them, particularly for people who are either reach-limited or budget-limited.
Micro 4/3 cameras are indeed competitive with crop DSLRs in many respects, but where crop DSLRs shine over micro 4/3 is in their autofocus system, which is a very fast phase-detection system. I expect micro 4/3 systems to continue to improve over time in this respect, though, so there may be some point at which crop DSLRs no longer have large enough advantages to remain competitive. It'll probably be a while, though.
Just kidding!
