Colorado offers hunts for as many species as any western state -- Rocky Mountain Bighorns, Desert Bighorns (residents only), Elk, Mule Deer, Whitetails, Lion, Antelope, Shiras Moose, and Mountain Goat.
Sheep, goat, and moose are all hard to draw, as are pretty much any sheep, goat, and moose tags. They're worth trying for, though.
Antelope is hard to draw, and the trophy quality isn't particularly attractive compared to an easy-to-draw state like Wyoming. Whiteail are mostly on private land on the eastern plains.
Colorado's elk herd is the largest in the nation. Trophy tags are hard to come by, but Colorado is the only state in the US that offers over-the-counter elk tags, making it a top destination. This, coupled with vast amounts of public land, make Colorado a great state to plan an elk hunt.
Mule deer are the other notable opporunity in Colorado. All tags are limited draw, but you can get a run-of-the-mill tag applying for it as your second choice. Premier mule deer tags take years of preference points to draw, but Colorado is considered the greatest producer of trophy mulies in the US right now.