Many have already been mentioned, but in terms of best zoos here are my picks:
Cincinnati Zoo–fabulous white tiger exhibit & I think they were first with the natural habitat thing.
San Diego–they also recently took over the Wild Animal Park (which is not in San Diego, but in Carlsbad). The Wild Animal Park is sort of like going on a safari–you can also camp there and hear the animals at night, which is cool. Only down side to SD Zoo & Wild Animal Park is the entrance fee, which is pretty hefty.
I also love the National Zoo in DC, but mostly because it is free and rarely crowded. You just walk right in like you are going to a park or something–no lines or anything.
In terms of worst zoos, the LA Zoo gets my vote. The exhibits are ugly and the animals are often missing from the cages. Also, there is no shade to be found as you walk around the park, so unless you like the hot sun beating down on you all day long–avoid this zoo. They have made some improvements, but it still sucks.