Mandarin is one example, among many others.
Verbs (and other word classes) do not change form, for any reason. That means no conjugations (subject verb agreement is a form of conjugation, so none of that either), and no plural/singular forms on nouns themselves.
There are ways to express more than one, by the addition of words, but is not strictly required and often restricted to people.
All other Chinese languages fall into that category as well.
Vietnamese, in another language family, also fits that description.
Japanese comes close. No subject-verb agreement, no plural/singular (although some nouns for people have collective forms, but it's not the same as a plural. example: kodomo = child or children, but kodomotachi = children in general, not a specific group). It does have conjugations, but not for reasons found in Indo-European languages. Changing the subject does not change the form of verb. Japanese has no tense, but it does have aspects, four voices, and many other forms that lack equivalents in English.
Note though that in Chinese languages, Vietnamese, and in Japanese, it's not quite as simple as one dog, two dog. They each have classifiers that must be used with numbers to describe nouns.
Japanese, for example, there are two possible structures:
one-[classifier for small animals] [particle turning a noun into an adjective] dog; two-[classifier for small animals] [particle turning a noun into an adjective] dog;
dog [particle, indicating things like topic, subject, direct object, etc)] one/two-[classifier for small animals]
However, without numbers, sentences like: I saw the/a dog(s) -- are identical. Choosing dog instead of dogs, a instead the, makes no difference.
The details work differently in Mandarin and Vietnamese (they both rely heavily on word order, unlike Japanese), but they use counters to work with numbers.