Today, dictionaries of most languages with alphabetic and syllabic writing systems list words in lexicographic order, usually alphabetical or some analogous phonetic system. 

In many languages, words are grouped together according to their true or normal origin ("root"), and these roots are arranged alphabetically. If English dictionaries were arranged like this, the words "import", "export", "support", "report", "porter", "port", "important" and "transportation" would all be listed under "port". This method has the advantage that all words of a common origin are listed together, but the disadvantage is that one has to know how to recognise all prefixes of a word before one can look it up. Some Hebrew, Sanskrit, and Arabic dictionaries work this way.

While most of Japanese and Korean dictionaries are arraged according to their phonetic writing (kana syllabic script for the Japanese, and hangul alphabet for the Korean), the main body of modern Chinese dictionaries mostly is still ordered according to the Chinese logographic writing system; but most Chinese dictionaries have an appendix ordering entries in accordance to the latin alphabet with the pinyin spelling, in order to allow readers to find words written in logograms whose pronunciation is not known. Chinese characters may be sorted according to one of many schemes based on the component parts of the characters (radicals, number of strokes, overall shape).

The first English alphabetical dictionary came out in 1604 and alphabetical ordering was a rarity until the 18th century. Before alphabetical listings, dictionaries were organized by topic, i.e. a list of animals all together in one topic.
retirement-
appoint

Bilingual dictionaries
Character dictionaries
Specialised dictionaries
Word order