Are there words that have no plural counterpart, because they are, in fact plural? Words like rice or scissors come to mind.
Your title asks for nouns that are always plural, but your question seems to ask for nouns that have no plural. I'll answer the latter first.
Non-count nouns are very rarely used in the plural. Some examples include butter, electricity, ballet, and indifference. You could say We tested six butters to see which was best for baking, but this is rare, and the others couldn’t be used this way.
(Many proper names are rarely pluralized, just because there’s only one. But it can be done: “The Sun is so large a million Earths could fit inside”; “there are two Americas, not one”; “it would take nine Chuck Norrises to bring down one Bruce”; “conformable as other household Kates”.)
As for nouns that are always plural, there are a few. Scissors and thanks come to mind. You never give somebody a single thank. Some more are listed here. (They missed dregs though.)
Rice is a mass noun, a noun that signifies unbounded amounts, such as liquid, small objects, and abstract or immeasurable concepts.
Due to a comment, I did some more research and since there is no singular form to rabies as it comes from the latin word rabiēs, from which we get the word rabid, it looks like it is also a mass noun not a plurale tantum. That final "s" can get confusing…
Yes. Other answers have already talked about non-count nouns, and as they mention, non-count nouns in English are generally singular and can be pluralized if it comes down to it. But genuinely plural words without a singular counterpart do exist.
The word mores (pronounced "MOAR-eaze" /ˈmɔriːz/, or by some people, "MOAR-ayze" /ˈmɔreɪz/) is derived from a Latin plural and remains plural, but the Latin singular form is never used in English (not even as a noun modifier, like scissor kick, billiard ball, dartboard).