It can be implied and unspoken, and often is in the imperative voice.
"Get out of here!"
Those are complete sentences, but the subject isn't in them, so if that's what you mean, there you go. But make no mistake. They do have subjects, just like the last sentence I wrote does.
UPDATE: I just noticed the last part of your question, and feel I should point out that the necessity of subjects is not unique to English; in fact, it's part of universal grammar. All sentences in all languages have subjects. Some languages have other ways of communicating the subject of the verb than with a separate word; for instance, many Romance languages do it through verb endings, but somehow or other, every language has a way of communicating who is doing the verb.