SUPPLEMENTARY:  
Bill Franke's answer is admirable, and this is not offered as an alternative; but there's a lot of historical and technical baggage behind the question of the English “subjunctive”, so a little clarification may be in order. 

At bottom it's a terminological dispute. 

*Subjunctive* in Latin (and Greek) grammar was the traditional name for **distinct inflections** of the verb used in specific syntactic and semantic contexts. Since in most of these contexts the clause which the verb headed was *subordinate*, explicitly or implicitly, to a main clause, these forms were given a name which indicated that they “subjoined” the clause; the distinction was categorized as one of *mode* or ‘mood’, opposed to other moods expressed with other forms: *indicative*, *imperative*, *optative*, *infinitive* are the terms employed by Dionysius Thrax in the 2nd century BCE.  

Many European languages maintain a distinctive set of forms employed similarly to Latin which it is not too far-fetched to call *subjunctive*. It is quite otherwise with English. In Present-Day English only one verb, *be* has as many as eight forms; most have only four or five; a handful have only one or two. In these circumstances the notions of *subjunctive* and of *mood* itself take on very different significance. Early (17th- and 18th-century) students were puzzled how to apply the Latin terms to English: some recognized *mood* as a category realized with auxiliary verbs, others denied the existence of *mood* altogether:  

> Now in English, there are no Moods, because the Verb has no Diversity of Endings, to express its Manners of signifying; but does all that by the Aid of Auxiliary or Helping Verbs which in the Latin, and some other Languages, is done by the Diversity of Terminations or Endings.  – Greenwood, *An Essay towards a Practical English Grammar* (1711)
>
> ([Here](https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CDIQFjAA&url=http%3A%2F%2Ffaculty.education.illinois.edu%2Fwestbury%2Fparadigm%2Fvol2%2FAuer.rtf&ei=emWOUbKAF4jBygHwzYC4CQ&usg=AFQjCNF8-AH8esv01UemR7P2TyXMsdxlCg&sig2=I57LXiw8CIEB2e3YCfnU3A&bvm=bv.46340616,d.aWc) is a fascinating study of 18th-century treatments of the subjunctive.)

Nonetheless, by the 19th century it had become usual and convenient to acknowledge a *subjunctive mood* in English, analogous to Latin, and to understand the specific forms elicited in *subjunctive* contexts as *subjunctive forms*. (I suspect this is because until very recently formal English grammar was taught primarily within a context of Latin literacy, and opinion gradually hardened around pedagogically useful concepts which aligned Latin and English usage.)  

Over the past fifty years, however,formal grammarians have turned their backs on this approach and endeavoured to develop models and terminology specifically suited to the description of English. Consequently, there are today a number of notions of just what the English *subjunctive* is. For those like me and Bill Franke, who were taught in the Old Style, *subjunctive* is in the first instance a name for the *verb forms*. For some formal linguists, *subjunctive* is a name for the *modal context* which elicit those forms: these will tell you that “Although English **clauses** may be subjunctive, English **verbs** are not”. And other linguists argue that the term itself is useless; other, happier terms account quite parsimoniously for most grammatical phenomena, and *subjunctive* survives in contemporary linguistics mostly as a name for the use of *be* in contexts such as that which the current question concerns—and even there it is often deprecated.