Rascal,
Woodland Park has done a really nice job of creating natural looking habitats. It's still a bit of a challenge to get shots that aren't obviously in a zoo, but as Rocky and Deb's shots show, with shallow depth of field and careful choice of location, you can do it. That's true of many of the animals, but not all, for example I've yet to find the elephants in a location that doesn't have a lousy background.
The twisty, windy and sometimes confusing network of paths can be annoying, but on the whole it's a great zoo.
A suggestion for local photographers... If you enjoy shooting at the zoo, buy a season pass. That way you can do what Deb and I did, and visit the zoo for a couple of hours without spending $25 or so to do it. On the other hand, even if you don't have a pass, it's not much more expensive than going to a movie, and well worth it.