The subjunctive mood

If I were
I wish I were

The first thing to get right here is the distinction between the subjunctive and the indicative.

The subjunctive is used in many languages to express 'unreal' event such as wishes, hopes, fears, judgement, opinion, necessity and so on. In this regard it is closely related to modality and you should see the sections on this site on modality and conditionals, both linked from the list of related guides at the end, for more in this area.
The indicative, with which we are not concerned here, is used to talk about real events and states.

Two questions:
Which of the following is subjunctive and which indicative?
How do you tell?
Click here when you have an answer.

It was important that he be there.
He was there.

The first is subjunctive because the speaker is expressing a view of the event rather than the event itself. It could have been introduced also by clauses such as
    I requested
    They demanded
    We recommended
and so on.
The second is an example of the past indicative and states what occurred with no expression of the speaker's view.

How do you tell?

If you look at the verb form, you will see that there is agreement between the subject and the verb in the indicative (the use of was rather than be in this case) but this is lacking in the subjunctive where the base form be is used.

Types of subjunctive

There are three:

The subjunctive in that-clauses
This is the example above. It is usually formal (arguably not so in American English) and is used to express the speaker's view that something should, must or ought to happen. (This is sometimes called the 'mandative subjunctive' because it expresses the fact that we are mandating.) Here are some examples:
1. I insist that he stay until the end
2. We recommended that they go to Delphi
3. I suggested that he visit me
4. I require he move
Notice that there are no third-person or past tense-endings on the verbs in these examples.
English speakers are not obliged to use the subjunctive in these circumstances because the rich modal system allows many alternatives:
1. He must stay till the end
2. We recommended that they should visit Delphi
3. I told him he ought to visit me
4. He has to move

The subjunctive in fixed expressions
These are usually left-over chunks of language from the time when English used the subjunctive much more frequently. These expressions are often very common and worth teaching as chunks of language rather than troubling learners with the grammatical explanation. You need to know that; they don't. Here are some examples:
1. So be it
2. I will finish come what may
3. Be that as it may ...
4. God save England
5. If need be
6. Perish the thought

The were and be subjunctive
This is common in some fixed expressions, following wish, in unreal conditionals and after certain subordinating conjunctions. Examples include:
If I were you ...
If you were to ask me ...
He speaks to me as if I were a public meeting
I wish I were rich
He used the wrench as if it were a hammer
I arranged for him to help lest the work were / prove too hard

In informal speech, the subjunctive were is often replaced by the indicative form: I wish I was rich etc. but this is not always possible and many would object to *If I was you ... but fewer might argue that I wish he was here is 'wrong'.

Let

It can be argued that the subjunctive occasionally occurs with the verb let in expressions such as
    Let it rain. It won't spoil my day.
    Let it snow (as in the song)
    Let him try
It can equally well be argued that this is a semi- or marginal modal auxiliary verb followed by the simple infinitive. That's how it is treated on the site in the guide to semi-modal auxiliary verbs, linked in the list at the end.

Optatives

Optative expression are those in which we express hopes and desires and these are natural partners for the use of the subjunctive because, by definition, optatives refer to unreal or unobtainable hopes, fears and wishes.
The subjunctive, for example, often occurs after the verb wish as in, e.g.:
    I wish I were 10 years younger
    She wished he were with her
and after items like If only as in, e.g.:
    If only she were rich
    If only I were a doctor
etc.
There are other optative forms which take the subjunctive and for much more, see the guide to suasion, linked below.

That's about it for the subjunctive in modern English.
Other languages make far greater use of the subjunctive. German and Dutch have two forms of the subjunctive, French, Spanish, Italian and Portuguese make great use of a range of subjunctive forms, as do Celtic languages, Arabic, Hebrew, Greek and Hungarian.
Speakers of these languages in particular need careful teaching of English modal auxiliary verbs because the subjunctive tenses they employ often take the place of a rich modal system.

Related guides
modality index	where you will find links to many guides to types of and ways of expressing modal concepts
condition and concession	for more on some uses of the subjunctive
mood	a brief guide to the meaning of mood and the three forms in English
semi-modal auxiliary verbs	for a guide which includes consideration of let and much else
suasion	for more about wish and other optative forms which are often combined with the subjunctive