Fish are probably the easiest classroom pets to take care of, as long as you have appropriate aquarium equipment. They are clean, completely silent and have no chance of escaping and causing a disturbance. You can make feeding the fish a daily task that students can sign up for, and changing the water a more involved weekly task. The disadvantage of fish is that they are not as much fun as animals that can be more interactive with students.
Most birds do not make good classroom pets because they are noisy and demand a lot of care and attention. However, finches and canaries can make good classroom pets in certain situations. If you get finches, they should be in pairs of the same sex. Canaries can be alone. They sing and do not require nearly as much attention as other birds. Get a large cage and have students take responsibility for feeding seeds to the birds.
Small mammals such as rodents are common classroom pets. They are inexpensive, easy to care for and most people aren't allergic to them. Get a guinea pig, gerbil, hamster or mouse as your classroom pet. Keep it in a cage with floor litter and a water container. Best of all, you can take the pet out of the cage and have students play with it. Small mammals are also easy for students to take home and care for over the weekend.
Although they might seem icky to some, amphibians can make very low-maintenance pets in the classroom. Newts, salamanders and frogs are all appropriate pets for the classroom. If you get an amphibian, make sure that students wash their hands well before and after handling them, as amphibians breathe through their skin. Amphibians are more exotic to children, so they might elicit more attention and excitement from them.