According to my understanding, all languages are expected to exhibit some aspect of an animate-inanimate dichotomy, and English is not an exception. The only question is to what degree and how such a dichotomy is expressed in the language.
Despite the derivation of the term, linguistic animacy is not determined only by whether something is alive or not. It appears to be correlated partly with whether something is normally a living being, but also with sentience, personality, and capacity for being a subject of empathy by the speaker in the broadest sense of the word "empathy." The specifics vary from language to language and are part semantic and part "social." Some languages are quite quirky in what is considered animate or not for unclear reasons.
Animacy usually exists on a scale from most animate to least animate, rather than being something completely binary. The exact criteria for what constitutes the scale will vary from language to language and the cutoff between animate and inanimate will also vary from language to language, from syntactic structure to syntactic structure, and situation to situation.
In English, the distinction between "he," "she," and "it" is a good example of what is partly an animacy distinction. Like other animacy distinctions in other languages, the distinction is made on a scale composed of complex criteria. For instance, a male "human after the age of a few months cannot be referred to by "it," even after death, except in very extreme circumstances. A newborn male child can, however, be referred to as "it" in some circumstances (E.g., "Do you see that baby all dressed in blue, it's so cute!"). A collection of male humans can also be treated as inanimate. (E.g., "The professional baseball union has to change its strategy to win the strike.)
Considerations of animacy can be seen in the fact that English speakers will more readily violate number agreement than animacy agreement. E.g., sentences like: "Everyone should do their part." have existed in English for many centuries, despite the violation of number agreement; however, you never find such sentences as "*Everyone should do its part."
Another scale example is the treatment of animals. Documentaries following a an animal family group almost always use gendered pronouns to refer to the individuals, whereas more "impersonal" or detached descriptions of animals will treat them as inanimate. Compare these two sentences: "The lioness is now affectionally greeting the other members of her pack as they are reunited after a long unsuccessful hunt." with "A lioness can be distinguished from a male lion because it doesn't have the long hair that comes with a mane."
Another example of animacy distinctions in English is the dichotomy between interrogative "who" and "what." Which pronoun you use is determined by animacy. Such distinctions need not be binary. For instance, relative "who" is marked for animacy; relative "that" can be used for both animate and inanimate referents; and relative "which" now prefers inanimate referents.
There are also subtler linguistic phenomena that can be classified under the rubric of animacy. For instance, consider the acceptability of these two sentences:
A. I was hit by a rock.
B. *The rock was hit by me.
Most or possibly all languages rate first person references extremely high on the animacy scale and generally use syntax that puts animate references before inanimate references when a choice exists. Animacy also tends to correlate with agency. In this case, sentence B feels unacceptable as an equivalent to "I hit the rock." precisely because it seems a violation of animacy rules that tend to require English speakers to take the view of animate referents using agency. On the other hand, you can say, "The rock hit me on the head" because the circumstance attribute a lack of agency to "me," lowering "me" on the animacy scale as it exists in English.
Because animacy works on a scale, we can be more comfortable with talking about a "person's leg" than a "*table's leg," while still being able to talk about both a "person's face" and a "clock's face. The criteria are complex and on a scale of acceptability.
And how does animacy work in other langauges that you know of (such as
French, German, Japanese etc.)
In French, German, and Spanish, there are nouns whose grammatical gender can conflict with natural gender or other gender tendencies. In all three cases, the choice of article may be fixed by the grammatical gender (e.g., "das Kind" (a neuter German noun phrase meaning "the child")); however, "long-range agreement" tends to follow natural gender. A similar feel can be seen in an English sentence referencing the New York Giants football team, where you could say: "New York has to get its offence going if they are going to win the game."
In Spanish, the object of a transitive verb is usually unmarked if it follows the expected animacy hierarchy and is used with a subject that is higher on the animacy scale (E.g., Yo amo mi casa (I love my house). When the expectation is reversed or subject and object are roughly equal on the scale of animacy, the object must be marked with "personal a" (e.g., yo amo a mi madre ("I love my mother) or esta página sigue a la otra "This page follow the other one").
In Japanese, for example, one verb is used to predicate the location or existence of animate referents (いる/iru), and another of inanimate referents (ある/aru).
In Mandarin, a direct object pronoun is normal when referring to animates, but normally omitted when referring to inanimates. Also pronouns otherwise distinguish singular and plural when referring to animates, but usually do not when referring to inanimates.
Arabic nouns often have much more complexity around number than English nouns.
A somewhat extreme case is the word شَجَر ("trees"), which has five different forms of number compared to the two in English (i.e. "tree" or "trees"). Despite this complexity in number, plural inanimates in Arabic are universally treated as feminine singular for adjective, pronoun, and verb agreement. Animate masculine and feminine words usually have plural agreement (Verbs, however, use singular forms when they precede the subject). In Arabic, all sentient beings are animate, but the line can also extend to include some animals. Human collectives, however (such as "governments") are treated as inanimate, despite their ability to exercise agency.