In Spanish, it is very common for the subject to not be directly stated, although it is implied by the conjugation of the verb. For example, the word hablamos, which means "we speak," can be a complete sentence. The subject of the sentence is not directly stated, although it is implied to be nosotros, which means "we."
In English, the subject can be similarly implied, although only when the verb is in the imperative mood, that is, when the sentence is a command. For example, the command "speak" is a complete sentence; the listener can infer that the subject is "you."
Exclamations, such as "ouch!" in English or "¡ay!" in Spanish can express a complete thought, although they generally are not considered to be sentences.