I've never heard anyone say "salmons" but it can be used as well as the plural form "salmon", so Paul is quite correct.
The same applies to "fish/fishes". Also "trout/trouts"; "mackerel/mackerels"; "cod/cods"; "plaice/plaices".
However, it seems to be more usual to say "there is a shortage of cod in the North Sea" and "salmon is plentiful in the River Dee". Obviously the plural definition is meant in both cases.
PS: In the UK, a "trout" doesn't always mean a fish, but we'll not even go there.... ;-)
Yes, I've heard of "old trout" and..."brown trout".
I hope you weren't talking about the latter ;-).
The statement that these words 'do not have plurals' is incorrect. Why? Look at these two sentences:
The deer is jumping over the fence.
The deer are jumping over the fence.
Run these by a native speaker and he or she will immediately know that there is only one deer in the first sentence, but two or more deer in the second sentence. While 'deer', 'fish', 'moose', and 'sheep' do not change form in plural, they do have plurals, or one would not be able to conjugate the verb according to number.
Among the words you listed, only 'cattle' actually doesn't have a plural form. "The cattle are grazing out back," is a grammatically permissible sentence, but "The cattle is grazing out back," is not grammatically correct in any dialect of English. One would have to say either, "The -cow- is grazing out back," or "The -bull- is grazing out back," depending on the gender of the animal. As further evidence for the difference between 'cattle' and the other words, one can say 'a fish', 'a deer', 'a moose', or 'a sheep', but one can never say 'a cattle'. One must always include the quantifier 'a -herd- of cattle' or 'a -drove- of cattle'.***
The difference between 'cattle' and the other words that have plurals, but do not change form according to number, is that 'cattle' is an inherently collective noun in a way that 'fish', 'deer', 'sheep', and 'moose' are not. The noun can never refer to anything except multiple cows or bulls. Two or more works, but never one.
Taking these words together, the reason that they don't have separate plural forms is purely etymological. When the Old English language still had a masculine, feminine, and neuter gender for nouns, words such as 'fish', 'sheep', 'swine', etc. belonged to the Strong Neuter declension. For example, the word 'fish' evolved from the OE word 'fisc'. The plural of 'fisc' in the Nominative case (OE had four cases similar to German) was 'fiscu'.
When the Normans invaded and forced a rapid, dramatic change in the development of the English language (grammatical gender and noun declension disappeared almost entirely), most nouns resolved to the regular plural formation of -s. Commonly used Strong Neuter nouns, however, never underwent this transformation, and instead dropped the -u in their plural forms. Thus 'fisc' - 'fiscu' became 'fish' - 'fish'. For this reason, the group of nouns that do not change form in plural is limited ( as far as I know) to animals. They were the only words common enough to resist sublimination into the regular -s plural.
'Moose' was actually imported from the Native American language Knisteneaux, it has absolutely nothing to do with the word 'goose', but since English speakers couldn't decide whether 'meese' or 'mooses' was the appropriate plural, the language merely settled for grouping it with other non-changing plurals.
As mentioned by other posters, the nouns you listed may sometimes take -s endings, but sometimes they can't. Do not worry about it for the moment. Just memorize them as words that don't change in the plural and be very careful to decline your verb according to the correct number (do not say "The fish swims in the sea" when you mean more than one fish).
*** Unlike other aspects of the language, quantifiers for groups of animals really are completely impossible to predict. This goes for native speakers of English as well; I have absolutely no idea what the correct quantifier is for a group of owls (Webster's Dictionary says it's a 'parliament'). One has a 'gander' of geese, a 'school' of fish, a 'pack' of wolves, a 'flock' of birds (or tourists!), a 'plague' of locusts, etc. And don't even get me started on how one conjugates the verb according to number for these groups. It's total madness and it completely changes depending on region.
And by the way, don't ever accept the explanation "that's just the way it is" for questions about a language, English or otherwise. Languages don't just spontaneously pop into existence. Their irregularities aren't placed there just to torment non-native speakers. Languages change and evolve according to observable, understandable shifts in pronunciation, grammar, and word formation. For modern languages with writing systems, it's quite possible to trace where a certain irregularity came from and why it exists.
Knowing the reason for an irregularity doesn't help much in learning a language. It can, however, relieve frustration, thus removing a barrier to learning.
More to the point, why is there an advert for 'Dairy and Beef Semen Online' at the top of this page? It beggars belief!
Because we're writing the words "cow", "bull" and "cattle". Perhaps because of "fence", "grazing", "sheep", "swine", "gender" and "animal" too. This is what happens when your ads are by Goooooogle.
"the group of nouns that do not change form in plural is limited ... to animals" we also have a number of more recent "borrowings" from languages which don't have distinct singular and plural forms, e.g., "samuri" ... no ... bad example, they're animals too (in a strict biological sense of course) ... "kimono".