Many mainstream "Non-dairy" creamers, like Coffee Mate and International Delight, usually have dairy in them though, specifically, caseinate. So not suitable for strict vegans. It's a quirk in labeling laws that products that have milk-derived ingredients can be labeled non-dairy as long as they label the milk-derived ingredients as milk-derived in the ingredients list.

That being said, they do make vegan creamer, never had any myself. It's still a specialty product though, most places that serve coffee, beyond coffee shops, are only going to have milk, half and half, and Coffee Mate/International Delight.