The official chart published by the International Phonetic Association is the official standard and thus should be used as the primary reference.
The primary difference between the official chart and the Wikipedia one is that the former is created to illustrate the set of symbols, while the latter simply lists the sounds found in the world's languages (though not exhaustive) about which Wikipedia articles exist.
The important thing to note is that the IPA does not provide a means to refer to specific sounds per se but a set of shorthands for classifications of sounds, organized based on how sounds are found to be made and used in languages. The current Principles of the International Phonetic Association states:
The IPA is designed to be a set of symbols for representing all the possible sounds of the world's languages. The representation of these sounds uses a set of phonetic categories which describe how each sound is made. These categories define a number of natural classes of sounds that operate in phonological rules and historical sound changes. The symbols of the IPA are shorthand ways of indicating certain intersections of these categories. Thus [p] is a shorthand way of designating the intersection of the categories voiceless, bilabial, and plosive; [m] is the intersection of the categories voiced, bilabial, and nasal; and so on. The sounds that are represented by the symbols are primarily those that serve to distinguish one word from another in a language.
While the distinct letters of the IPA are chosen so that they represent sounds "that serve to distinguish one word from another in a language" (known as phonemes), the IPA also provides diacritics to modify them so that it can be used to refer to finer shades of sounds.
The Wikipedia chart exploits this flexibility of the IPA to show links to the articles about phonetic sounds. So that chart should not be taken as a chart of the alphabet or its possibility, but of the articles about phonetic sounds that exist on the site.