If humans disappeared what animal would occupy its place

Is there any species that can?

I think the usual answer is the cockroach. If we suppose that whatever causes our own species to die will take out anything else that is like us at the same time, then the only survivors will likely be all the small but tough creatures (represented by roaches) that have already survived previous extinction level events.

If the oceans aren't too badly harmed by "whatever kills us" then some oceanic versions of the roach may continue on as well.

If you meant the question in a purely theoretical sense where mankind is merely erased by magic like in recent TV specials and leaves all else intact, then any number of carnivores will become local alpha species. Canine packs will have an advantage in some places. We pulled off a pretty fancy trick in mastering the entire globe to some extent. Rin Tin Tin is not going to become King of the New World after we're gone though. Don't expect doggie governments or dolphins arising from the deep or such things. Most likely the ecology around Earth will settle into a boring balance until the next extinction after that.

None. The second smarter animal other than humans, are dolphins, and their need for water, and lack of fingers will not allow them to evolve in a way that it could be consider a human replacement.

Chances are it would still be a primate. Having thumbs is critical to being able to alter your environment so is a large brain. Given enough time, eon, maybe we would evolve once again. Scary huh.

Id say dogs who knows what thay can do

NONE
Of course there isn't.

I would have my money on the birds.