I do the zoo thing a lot, and for me it mostly comes down to forgetting I'm taking a picture of an animal and just taking a portrait of an individual. Getting an expression, an attitude, or an action is what will make or break the shot. Does the personality, as it were, of the individual come through?
Where the fact that it's an animal makes a difference is that you're more limited in communicating with your subject. So you have to have patience and learn how to stalk in a friendly manner that doesn't make your subject nervous or upset. Reading and projecting body language is part of it. But overall, patience. If you're interested in your subject, it generally won't take them long to do something photoworthy. Be ready, but also learn to sit still for a while.
Technique-wise, I mostly shoot with primes, and go for selective focus and getting the eyes sharp, just as I would for any other portrait.
I get my best shots at the zoo when I'm willing to hang around an enclosure for 15-30 minutes. Most folks want what they want right now. So they go home with a camera full of very boring shots of exotic animals when they go to the zoo. I'm willing to wait to get a shot I like with the light and background I want, on their schedule.
And, obviously, if you're going to do wildlife, this all gets exaggerated even more (plus, y'know, the necessity for long lenses). At the zoo, 15-30 minutes is enough. Out in the backcanyons, it can be months before you're there on the spot.
Then again, some of them are just hams.
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