The most common negative prefixes in English are in-, un-, non-, de-, dis-, a-, anti-, im-, il-, and ir-. While some of these prefixes are interchangeable in some uses, there are subtle differences between them.
in-, im-, il-, ir-
The in- prefix (from which im-, il-, and ir- are derived) is generally the least useful of the negative prefixes, as it only goes with certain Latin-derived stems (e.g., intolerant, inarticulate, impenetrable), is highly conventionalized, and is identical to morphemes used in words that are not negative (as in inflammable, which means the same thing as flammable; irradiate, which means to expose to radiation; and illuminate, which means to make luminous). Thus, in- and its derivatives generally aren’t useful for creating new words.
The prefix non- is the most useful negative prefix, as it can be attached to virtually any noun, verb, adjective, or adverb and is not confusable with other common morphemes. Unlike in-, and un-, which often create nonabsolute negatives, non- is generally used to create a word that describes the complete opposite of its nonnegative form. In other words, for example, a nonconformist is someone who absolutely does not conform. If we were to coin the nouns uncomformist and inconformist, they wouldn’t have the same sense.
When affixing non- to a word, no hyphen is needed unless the stem is a proper noun. Spell-checkers might catch any unhyphenated non- words you invent, but this doesn’t mean your coinages are incorrect.
de-, dis-, a-, anti-
The prefix de- is usually affixed to verbs to denote reversal of an action. The prefix dis- is similar in some uses to de- and in other uses to un-. A- is affixed to adjectives ending in -al. Anti- means against.