(Based on Cory Taylor's paper: Functions of the Conjunctions of the Greek New Testament)
Ascensive [even] - expresses a final addition or point of focus. Usage usually determined by the context.
Causal [because, since] - expresses the basis or ground of an action
Comparative [as, just as, in the same way, thus, in this manner] - suggests an analogy or comparison between the connected ideas or tells how something is to be done
Conditional [if] - introduces a condition in the presentation of the speaker that must occur before a certain action or conclusion can occur. This conditional clause may not reflect reality, but rather simply the writer’s presentation or perception of reality. As part of a conditional clause this conjunction introduces the protasis (or if part of the if . . . then statement).
Connective [and, also] - simply connects an additional element to a discussion or adds an additional idea to the train of thought. Translated and, though if it is emphatic, it can be translated also, indicating a key addition.
Content [that] - involves a conjunction that introduces a subject, predicate nominative, direct object, or an appositional noun clause. Direct and indirect discourse are specialized object clauses following verbs of expression or perception. If introducing direct discourse (e.g., a recitative ὅτι), the conjunction may be left untranslated.
Contrastive [but, rather, yet, though, however] - suggests a contrast or opposing thought to the idea to which it is connected
Disjunctive [or] - gives an alternative possibility to the idea to which it is connected. Can suggest opposite or related alternatives
Emphatic [certainly, indeed] - appears in various forms and is determined by the context. Usually involves intensifying the normal sense of a conjunction. ἀλλά intensified is translated certainly; οὐ with μή becomes certainly not or by no means; οὖν becomes certainly.
Epexegetical [that] - involves a conjunction introducing a clause that completes the idea of a noun or adjective. It often functions like an epexegetical infinitive.
Explanatory [for, you see, that is, namely] - indicates that additional information is being given about what is being described
Inferential [therefore] - gives a deduction, conclusion, or summary to the preceding discussion
Local [where, from where, the place which] - gives the location or sphere (metaphorically), that is, the context in which an action takes place
Purpose [in order that, with the goal that, with a view to, that] - indicates the goal or aim of an action
Result [that, so that, with the result that] - gives the outcome or consequence of an action. The focus is on the outcome of the action rather than on its intention.
Temporal - gives the time of the action. Translation varies depending on the conjunction
Transitional [now, then] - involves the change to a new topic of discussion. Can often be translated now (though οὖν is frequently translated then).