The following is from Vine's "You can learn New Testament Greek":
In English the Subjunctive Mood expresses supposition, doubt or
uncertainty, and follows the conjunction if, lest, though, etc. In
Greek the scope of the Subjunctive is much wider. ... The following are
the principal uses of the Subjunctive Mood in the New
Testament: -
I - It is used in clauses expressing purpose. These are known as
Final Clauses (i.e., as having an end or object in view).
They are introduced by such conjunctions as hINA and hOPWS, each of
which means "in order that," or simply "that," and
negatively by hINA MH or hOPWS MH, "in order that not" or "lest,"
or even by MH alone, which when so used means the
same thing. [Note: This is what we have in Romans 6:4]
II - The Subjunctive is used in certain Conditional Clauses (these
are introduced in English by "if"), which imply either
possibility or uncertainty with the prospect of decision. ... (uses
EAN or EI)
III - The Subjunctive is used in Clauses Beginning With A Relative
Pronoun Or Adverb, like "whoever," "whenever," or
"wherever," which do not refer to a definite person or thing; in
other words, when the word "ever" can be used after the
relative. ... (AN or EAN follows the relative)
IV - The Subjunctive is used in Deliberative Questions, i.e., when
persons are deliberating as to what is to be done. This is
known as the Deliberative Subjunctive. Thus, "Shall we continue in
sin? (Romans 6:1)
V - The Subjunctive is used in Certain Forms Of Exhortation. This
is called the Hortatory Subjunctive. In English it is
introduced by "let." Thus 1 Thess. 5:6 "Let us watch and let us be
sober."
Additional uses:
1. In exhortations in the 1st person, including negative
exhortations with MH. Jn. 19:24 "let us not rend." (see V above)
2. In prohibitions the aorist subjunctive is used with MH as an
alternative to the imperative.
3. Similarly in requests.
4. In deliberative questions or those expressing doubt. (see IV
above)
5. Strong denials take the aorist subjunctive with the double
negative OU MH.