The class of arthropods that has one or two pairs of antennae is Crustacea. Crustaceans, such as crabs, lobsters, and shrimp, typically have two pairs of antennae. The first pair, known as antennules, are usually shorter and are used for sensing the environment. The second pair, called antennae, are longer and are used for touch and taste.
In contrast, Arachnida (spiders, scorpions) do not have antennae; they have chelicerae instead. Diplopoda (millipedes) have one pair of antennae, and Insecta (insects) also have one pair of antennae. Therefore, the correct answer is Crustacea.