I can't decide if the word 'clothes' is countable or uncountable. The dictionary only writes - plural.
Clothes, like (eye)glasses, pants, scissors, &c., is a plurale tantum—a word that only occurs in the plural. Most pluralia tantum in English are things that naturally conceptually come in pairs (two lenses in glasses, two legs in pants, two scissor-halves in scissors), but there are plenty of others—clothes, riches, remains, &c. Whether they're count nouns or not depends on how you define count nouns versus mass nouns, but in English they're generally considered mass nouns—they certainly behave like mass nouns in that you need measure words when you actually count them (three pairs of pants, not three pants).
The reverse is a singulare tantum—a word that only occurs in the singular. In English all mass nouns that aren't pluralia tantum are singularia tantum, and almost all singularia tantum are mass nouns—the only exception I can think of is a shambles.
(Even though this question asks about an English word I feel it's in scope because it's about a grammatical concept, not a usage question.)