Plain corn the kind you eat right off the cob always is gluten-free. Corn in most other forms usually is gluten-free, too, but not always.
Corn is a type of grain, but it's from a different branch of the family than the gluten grains wheat, barley and rye. Corn contains a substance known as "corn gluten," which isn't the same gluten that bothers people with celiac disease and gluten sensitivity. You can learn more about different types of gluten in What Is Gluten?.
Corn dishes that contain no other ingredients i.e., corn on the cob or sweet corn niblets shouldn't contain any gluten, as long as the corn was protected from cross contamination with gluten while it was being processed and prepared.
Most frozen canned products, even creamed-style corn (which most companies make with corn starch and sugar), appear to be gluten-free by their labels. But depending on how sensitive you are, you may want to contact the manufacturer to determine if the corn is processed on equipment or in a factory where there's gluten present.
Corn meal should be safe, but again, you'll need to check with the company to determine if it could have been cross-contaminated in processing. Bob's Red Mill is one company that produces corn meal that's processed in a gluten-free facility.
Don't assume commercially made corn muffins are gluten-free. Unfortunately, most recipes for "corn" muffins include more wheat flour than corn meal!
The same goes for other commercial products made with corn meal or other corn-based ingredients: unless it's specifically labeled gluten-free, you'll need to confirm the product's gluten-free status with the manufacturer.