From an LDS article on marriage:
The covenant of eternal marriage is necessary for exaltation. The Lord revealed through Joseph Smith: “In the celestial glory there are three heavens or degrees; and in order to obtain the highest, a man must enter into this order of the priesthood [meaning the new and everlasting covenant of marriage]; and if he does not, he cannot obtain it. He may enter into the other, but that is the end of his kingdom; he cannot have an increase” (Doctrine and Covenants 131:1–4).
It is unclear to me if only the highest of the three heavens described here is considered as exaltation or if the "other two" are lesser degrees of exaltation. It appears, from the first statement, that the unmarried cannot be exalted at all.
From what appears to be a catechism of sorts:
What must we do in order to obtain the highest degree of the celestial kingdom? (Students should identify the following doctrine: In order to obtain the highest degree of the celestial kingdom, we must enter into the new and everlasting covenant of marriage.
This catechism puts the "highest degree of the celestial kingdom" into the same category as Joseph Smith's statement puts "exaltation".
Can an unmarried LDS be exalted and, if so, is their exaltation of a lesser degree than the married?