For a while I've been aware of a particular piece of linguistic evidence - namely, that cross-linguistically it is common for the imperative (command) form of verbs to be shorter than other forms, seemingly lacking inflectional affixes applied to other conjugations. For example, in Old English, the verb 'creopan' (infinitive form) is 'creope' for first person singular, 'criepth' for third person singular, but 'creop' for imperative singular. This led me to hypothesize that language might have begun as commands, and later evolved to support more general types of expressions by the addition of affixes or extra words.
Think about the significance of this for a moment. One of the most frequent differences between normal sentences and imperative sentences is that the imperative usually does not have a (stated) subject, while, depending on the language, general sentences may require subjects.
Now, one of the big mysteries of linguistics is how we came to have such radically different language systems as accusative, ergative, and topic-comment*. Yet if commands were all that was originally spoken, this provides us with a trivial answer: initially, there was only a direct object and no subject, thus that language would predate the differentiation of the three types.
As the language evolved further, eventually there would be the need to add in a subject; how exactly this was handled would then determine which of the three paths was taken. Accusative languages would place the subject in a separate case (nominative) from the direct object (accusative case). Ergative languages would classify the subject based on whether its role is the agent (ergative case) or patient (absolutive case). Finally, topic-comment languages would place the subject (the topic) completely apart from the rest of the sentence (the comment).
*Since I don't think I've talked too much about topic-comment structure, I'll briefly explain here. In topic-comment languages, a topic is stated for a sentence or set of sentences, then a number of comments are made regarding that topic. Japanese, Korean, and Chinese are like this, among others, although it's also possible to use a periphrastic form in languages like English (e.g. "As for the movie [the topic], we'll meet at 2 [the comment]").
Of particular relevance, one thing the topic can be used for is the subject of the sentence, e.g. "As for him, he'll be coming later" (though true topic-comment languages usually wouldn't duplicate the subject as English does - it would be more like "As for him, will come later"); this is frequently done in Japanese and Korean, for example. Of course, the comment may have a different subject than the topic, so topic-comment languages may also be accusative or ergative (e.g. Japanese is accusative). Here I am hypothesizing that initially the subject was represented exclusively as the topic, then further evolution allowed the subject to be within the comment itself (although whether this is true is relatively unimportant to the theory that languages began as commands).