Languages can be classified based on different kinds of criteria. The most common are based on phonological, morphological, or syntactical criteria.
An important concept in linguistic typology is a linguistic universal. Universals make statements that are true of all languages, and may either be absolute (no language uses the raspberry sound phonemically) or implicational (languages with trial grammatical number also have dual grammatical number). However as most of what are called 'universals' have at least a small number of exceptions, it is often more meaningful to talk about tendencies (e.g. SOV languages are very likely to be postpositional). Note that one reason it is worthwhile to preserve dying languages is because many of what we now think are universals may turn out to only be tendencies, thus making us more aware of what can and can't occur in human language.
Certain phones occur often, while others are much less frequent, and some are more likely to be contrastive, while others usually group together with other phones as a single phoneme.
An example of a common phoneme is /t/. The overwhelming majority of languages possess it, though Hawaiian is an exception.
There are roughly four kinds of morphologies that languages use: Analytic, Inflectional, Agglutinative, and Polysynthetic. Morphological classifications are made based on how the morphology of the language works, that is, how are words formed, combined, and inflected (if they are).
Analytic languages are not inflected, that is, nouns and adjectives are not declined and verbs are not conjugated. Instead, the order of the words determines grammatical relationships. English is an analytical language, though not perfectly so, because there are some agreement markers, tenses, etc in English. For example *he do is incorrect, because to do must be inflected to mark third person singular subject: he does. Chinese can also be said to be an analytic language, though words are so little inflected in Chinese, that some would classify it as a minimal grammar language. This is incorrect, since what languages lack in inflection (or morphology) they must make up in word order, or syntax; in a technical sense, both morphology and syntax are considered to form parts of grammar. Both English and Chinese rely on syntax, word order, to show grammatical relationships, e.g. the subject must be in a certain position relative to the verb (in English, it must precede it).
Inflectional languages are different from analytic languages, because they do inflect (as the name suggests) quite a lot. A good example is Latin, in which most words are marked up and down for all kinds of tenses, moods, cases, agreements, and more. When the words in the sentence are inflected to show agreement with all their subjects, objects, and other arguments, then word order becomes very fluid. Whereas analytical languages rely on strict word order, inflectional languages have flexible word order.
Agglutinative languages are those in which words can be combined easily. For example, instead of saying the shoe of the horse, agglutinative languages say horseshoe. Agglutinative languages include German and Turkish. In these languages, new words are formed by combining old ones, so that words can become very long, but also contain a lot of information. This kind of morphology is called productive, because new words are formed in a predictable manner. Agglutinative languages can have both lots of agreements and inflections, or have rigid word order, such as German.
The last kind of morphological category, polysynthetic languages, is the least understood by linguists, because none of the major written languages in the world today, such as English, Chinese, Russian, Arabic, Hindi, etc, are polysynthetic. Some Native American languages in North America, such as Navajo, and some Polynesian languages are polysynthetic. Words, especially verbs, in these languages also tend to become very long, because every argument in a sentence is inflected on the verb, but also on other words with an argument structure, such as prepositions. These languages are very difficult to learn, not only because they are not properly understood, but also because one verb has literally hundreds of inflections. For example, the average Navajo verb has about 15 categories of prefixes, and a couple of affixes. These categories in turn, have between six and 200 members. In addition, the affixes can move around and change in agreement with other prefixes.
In reality, no natural language belongs exclusively to one category. Japanese, for example, has analytic pronouns (it uses postpositions to modify the role of nouns in a sentence), but inflectional/agglutinative in its verbs (taberu means to eat; tabenai means to not eat).
Syntactic typology distinguishes languages based on their preferred word order. The most commonly considered phrases considered are the subject, object, and verb. This gives six different possible orderings: SOV, SVO, VSO, OSV, OVS, VOS. The most common orders are SOV and SVO, constituting about 40% of languages each, with VSO constituting about 15%. The remaining five percent of languages have the object before the subject.
English and Mandarin Chinese are both commonly-spoken languages with SVO order. In Mandarin, for example, the simple sentence
(1a) Wǒ kàn shū
(1b) I read book
shows the same order as English, with the subject sentence-initial and the direct object following the verb.
By contrast, the about equally-common SOV order is found in languages such as Hindi/Urdu, Japanese, and Korean, among others. In the Japanese sentence
(2a) Watashi-ga hon-o yomimasu
(2b) I.subj book.obj read.polite
the verb appears in final position.
Some linguists have theorized that these orders are generalizations of a more general parameter on headedness. (The head of a phrase is the word which determines its type (e.g. in in the house the head is the word in, which creates a prepositional phrase.) The theory is that the verb serves as the head of a verb phrase containing it and the object, and the subject combines with this phrase to create a sentence. By this logic languages with right-headedness are SOV, and those which are left-headed are SVO.
However, VSO languages, such as Classical Arabic, Welsh, and Tagalog, cause problems for this theory. Consider the Welsh sentence:
(3a) Siaradodd Lloyd y Gymraeg
(3b) speak.past Lloyd DEF Welsh
It is not immediately clear how the verb could combine with the object to form a phrase without also combining with the subject. While more could be said about this, it should be clear that word order typology is important for understanding how sentences are parsed.