These days (and even back in the 1970s, when I was a zookeeper), most zoos (I'm not including roadside wild animal parks in that category) have very deep dry moats (usually ten or more feet deep and six or more feet across) as well as a fence between the public walkways and the enclosures of dangerous animals. It's not an easy thing to get into those enclosures. You not only have to be very stupid, you also have to be very determined.
I have a lot of stories like the ones in Donuel's opening post from my time working as a zookeeper. But I'm not going to tell them. Most of them are too depressing.