If the world was overrun by zombies the logical conclusion would be only waterborne life would be left. Due to the fact that they don't make sound and are presumably out of range for any of the dead to know they are there (or at least that makes sense to me.) With that in mind if humanity were to fall to zombies wouldn't it be logical to assume that all of our man made structures would wither away and decompose overtime allowing earth to reclaim itself?
Most animals wouldn't be negatively affected by a zombie apocalypse.
A critical trait of human hunting ability is our intelligence. If humans are unable to use tools, follow tracks, lay traps, or plan all but the most infirm animals would be able to easily escape. Without the pressure of overfishing, habitat depletion, poaching, and the exotic pet trade many endangered species populations would begin to increase.
The only species that wouldn't do well in such a scenario are those we have domesticated or critically endangered species that have repopulation programs.
If zombies took over the world, and are the standard type (shambling, dumb creatures without superpowers or etc), then they wouldn't do a lot to existing structures. The War against them, however, would. As governments attempt to exterminate the plague, they could nuke every infected city and reduce the world to a radioactive wasteland. Or, they could use conventional bombs to try to rid them from the air.
Wild Animals probably won't die out, unless the zombies use herding methods to kill them.