At the risk of sounding somewhat "Darwinian", as Ken Beesley puts it, I will very hurriedly try to add some data to the discussion on transitivity. It's certainly not practical to do a real language count, since data for most languages spoken on this planet is simply not available. However, I have some familiarity with the transitivity aspects of several of the more widely spoken languages.
Basically, if we limit ourselves to "major" languages, then we would conclude that transitivity is always marked. In other words, a verb cannot be used both transitively and intransitively without some morphological or lexical indication of the change in usage. I do not know of a single language that goes against this trend in a regular and productive manner. For most (all?) languages, such freedom is either totally denied, or is irregular and/or idiomatic. (Some people have claimed that English and Chinese allow verbs to be used both transitively and intransitively. In both languages, however, such use is idiosyncratic and irregular as I will illustrate below. However, Old Chinese DID have considerably more freedom in this regard than Modern Chinese.)
The most common way of marking transitivity is similar to the way Esperanto does it; i.e., affixes convert from transitive to intransitive or vice-versa. Turkish, Quechua, Swahili, Japanese and many, many others fall into this category. Some languages perform the conversion in only one direction; e.g., Fijian has verb roots that are inherently intransitive and adds an affix to convert them to transitive verbs.
Other languages, such as Arabic and Indonesian, have basic roots that undergo morphological derivation to create transitive and intransitive verb forms. In fact, Arabic makes more distinctions than any other language I am aware of (transitive/causative, intransitive/reflexive, causative reflexive and one or more others), although these derivations may no longer be as productive as we would like for an artificial language.
Romance languages such as French and Italian use reflexive clitics, and Russian uses reflexive affixes. German allows some freedom, but not as much as English - it often uses a reflexive construction, or morphologically derives a new verb with a prefix. Probably ALL languages have irregular forms, such as English "kill/die" and "drop/fall".
English is not nearly as productive as you may think. In fact, for many verbs, it is very nearly idiomatic. Consider the following examples:
He broke the window. = transitive The window broke. = intransitive (In modern Mandarin Chinese, two different forms of the verb "broke" would be needed for the above example.) He smashed the window. = transitive *The window smashed. = intransitive (ungrammatical) He built the doghouse. = transitive *The doghouse built. = intransitive (ungrammatical) He painted the doghouse. = transitive *The doghouse painted. = intransitive (ungrammatical) She flew the plane. = transitive The plane flew. = intransitive (this is gramatically correct, but is actually a middle voice construction) She drove the car. = transitive *The car drove. = intransitive (ungrammatical without adjuncts - this is also a middle voice construction) He climbed the mountain. = transitive *The mountain climbed. = intransitive (ungrammatical) The tree fell. = intransitive *He fell the tree = transitive (ungrammatical)In other words, it works for some but not for others, even when it makes perfectly good sense semantically.