We often visit Taronga Zoo in Sydney Australia. There are a number of open spaces where the animals are not behind a fence. If you use a good telephoto lens Then the opportunity may arise for a decent photo. The zoo put on a bird show where a number of native birds are displayed and fly around in an open area.
I set myself up to be near a tree branch where I knew a number of the birds would fly to and perch. Similar to staking out a water hole in the Australian bush to wait for the animals to appear.
I was lucky enough to capture a number of photos from this vantage point but my favourite is this one where the cockatoo has extended his (possibly her) crown for the photo.
I was shooting Olympus OMD E-M1 with the 40-150mm PRO lens at 180mm, 1/200 sec at f/5.0.