You do not have to conjugate the subjunctive mood with the leading 
que, but you'll frequently find the conjunction in that position when the verb is used in a sentence.  If you look at most textbooks and online sources, the leading 
que is not included in the conjugation charts.
 
You listed only the present subjunctive mood above (which is correctly written), except that the subject pronouns 
usted and 
ustedes are missing and there's no provision for 
nosotras and 
vosotras. There are two more subjunctive conjugations - preterite and future (and the preterite has two variations). 
 Que yo vaya
 
Que yo vaya (by itself) = Would that I could go, that I might/may go
 
When used in a subordinate clause, as in, 
él quiere que yo vaya, the translation is 
he wants me to go (or the dying English subjunctive 
he wants that I go).