This is my to hunt with bow someday list:

All types of bears (including in different countries)
Mule, Blacktail, Whitetail.
Coyotes
Wild Pigs/Boars
Elk
Carbiou
Squirrels
Rabbits
Groundhogs
Goats
Sheeps
Mountian lion (when and where legal)
bobcats, lynx
Javalins

Ok in short pretty much anything that can be taken legally by bow [:-]