Squash is a good companion for corn because the sprawling squash vines offer a living mulch to your corn. This keeps weeds down and retains soil moisture.
Beans are a great companion plant for corn because they fix nitrogen in the soil and corn is a heavy feeder of nitrogen.
Peas are another legume that fix nitrogen in the soil, making is a perfect companion plant for corn.
Similar to squash, cucumber vines grow well near corn. The vines can also help deter raccoons.