Haven't read the other responses yet aside cascademn's. I choose "other" because if Humans went away at this point in time, I see it as a
interdependent combination result and wiping out of other all
known species happening thusly:
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Weapons of Mass Destruction: WMD which destroys all or near all but will result in either all humans gone or struggling to survive and may ultimately not succeed or fail initially as genes fight to survive and adapt to the new environment. So, perhaps not an exact *new* species but the newest evolution due to the factors aforesaid. This has resulted in removal or initiated removal of centric species of the areas involved. The result of less of them in their environments have allowed less mating + food from others on the respective food chain thus high survial is lessened or gone.
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Disease: same as above, except with diseases already running amok with our genes and encroaching upon humanity's doom with or w/o WMDs. Intermixing of relatively healthy + diseased (recessive or not) human genes. Even 100% healthy + 100% healthy (I highly doubt that there is such a 100% but let's just go with it) will not matter considering the state of the environment + current nutrition (processed foods etc) + technology with EMW (electromagnetic waves but I'll get to that below). This relates to animals we rear and produce in order to eat and others who feed of of altered animals which we have abanonded. Certain animals (ex. cows/chickens/pigs) have become so distorted due to narcotic drugs intended to make them grow faster (etc etc) which has resulted in some diseases among them. Ex. Mad Cow Disease and certain other birds which have intermixed-mingled and carry new diseases. Same thing with Insects such as flies (like mosqitos and then go infect humans from diseased blood and diseased environments). All other animals are affected in a similiar manner too (whether by over hunting/loss of prey/etc/polluted "nutrition" from their enviornment's have alterted them. Not as apparent but still has)
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Technology: EMWs (aforesaid)/radio waves etc have not only affected humans, with creating cancers (such as brain cancers from cell phones etc) but have proven or are suspected largely of getting rid of birds (I recently heard on the news about this for Toronto's birds disappearing) and probably other creatures (as it's not too far of a jump to suspect they'd get affected too).
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Environmental-Ecosystems: Due to all of the above and others such as clear-cutting (resulting in even more species loss from habitation loss), toxcitiy/pollution (deliberate or incidental). We've tampered so much with the specific natural patterns of ecosystems of both our own and all species on Earth above and below and new ones forthcoming. New species are being found, intermixed from known ones and ones that are still being determined as to how they now exist (especially of deep sea life creatures, both mammalian + plant etc). Plus alllllll Enivornmental disasters which not only affect us but all species too.
So, I doubt that any of our current species will be exactly as they were, assuming they survive us, there will be new ones made out of the mix of pre-existing ones or some new one which developed over bacteria over time. Who will reign? The one who
exceedingly multiplies the fastest and is capable of destroying the other species as humans did (are doing)

But this is ONLY if they become conscious or are capable of perception. As we've seen, ecosytems were put in place to ensure no species dominated any other. I wouldn't have even said that dinosaurs dominated. They were just the "biggest". They weren't conscious of taking over the enivornment. They didn't exterminate the other species, they fed and were interdependent on them.
If humans did not evolve into a creature able to interpret its own consciousness, we wouldn't even be rubbing sticks. There is evidence of female primates (chimps) breaking branches off trees and turning them into weapons to hunt with. Perhaps, they will be the ones as nature is inherently getting rid of us due to natural disasters. If they survive, perhaps they will, in time, become the next humans minus the larger time span to evolve b/c we'll have left behind things that they will first "play" with and then perhaps learn to perceive + understand (maybe 20 thousand years instead of our supposedly 70 thousand + a shorter *leap* than ours were these past 6 thousand years of civilisation). Assuming there is any type of structural evidence we were here to begin with. Anything less than Aliens (hummanoid/repitilian/Atlantians/w/ethe hell we cannot perceive at this time) or a gigantic comet or numerous comets/w/e from space to destroy this planet. Aliens may come before we're gone and gigantic comets may destroy Earth completely.
I've read that people want to send garbage to space. I suspect if that should happen that the garbage, assuming we survive and other existing Earth life survive including bacteria or the last single-cell at the moment, will then have morphed or become organically alive and shoot back to Earth to destroy or inhabit (inorganic or organic) or just lay dormant as bacteria alter it and...
The New Humans shall roam again, evolve and control, distort and destroy as it's all cyclical!
