Why does Hippolyta want to marry Theseus in A Midsummer Night's Dream?

Hippolyta wants to marry Theseus in Shakespeare's A Midsummer Night's Dream because she loves—or, maybe not.
There are a number of versions of the Theseus/Hippolyta myth that lead up to A Midsummer Night's Dream which might help explain the relationship between Theseus and Hippolyta.
At some point in the mythical past, there was a battle between Theseus and the Amazons, commanded by Hippolyta. The Amazons were defeated, and Hypployta was taken one of several ways; either Theseus took Hippolyta as his prize for defeating the Amazons, Theseus simply abducted her, or Theseus asked Hippolyta to marry him and she politely declined, and then he abducted her. In any one of these three versions, Hippolyta is in Athens with Theseus under duress.
There's also a version of the myth in which Theseus plans to marry Phaedra instead of Hippolyta. The rejected and enraged Hippolyta organizes the Amazons to attack Theseus at the wedding ceremony, and Hippolyta is killed in the attack. Since Hippolyta is alive and well at the start of A Midsummer Night's Dream, we can eliminate this version of the myth from consideration.
A more romantic version of the myth is that Hippolyta was in love with Theseus before he attacked the Amazons, and she betrayed the Amazons by running off with him. We'd like to believe this version of the myth—because this is a comedy, not a tragedy—but Theseus tells Hippolyta very near the beginning of the play:

THESEUS: Hippolyta, I woo'd thee with my sword,And won thy love doing thee injuries (1.1.17–18)

which brings us back to one of the Theseus-defeats-the-Amazons-and-abducts-Hippolyta versions of the myth, although we're led to believe that, somewhere along the way, Hippolyta actually fell in love with Theseus. In other words, Shakespeare made up his own version of the story, which is something he did with just about every play he wrote. (The Tempest is Shakespeare's only entirely original play.)
At the start the play, Hippolyta echoes Theseus's feelings about their upcoming marriage:

THESEUS: Now, fair Hippolyta, our nuptial hourDraws on apace; four happy days bring inAnother moon; but, O, methinks, how slowThis old moon wanes! She lingers my desires,Like to a step-dame or a dowager,Long withering out a young man's revenue.
HIPPOLYTA: Four days will quickly steep themselves in night;Four nights will quickly dream away the time;And then the moon, like to a silver bowNew-bent in heaven, shall behold the nightOf our solemnities. (1.1.1–11)

Hippolyta doesn't seem overly enthusiastic about the wedding, but she goes along with Theseus's happy anticipation of the "solemnities."
Nowhere in the play does Hippolyta actually say why she wants to marry Theseus. She says only that she's looking forward to marrying him, generally, and that she has a good feeling towards love, even after she hears about the merry mixed-up love of Hermia, Lysander, Helena, and Demetrius:

HIPPOLYTA: But all the story of the night told over,And all their minds transfigured so together,More witnesseth than fancy's images,And grows to something of great constancy,But howsoever strange and admirable. (5.1.24–28)

In trying to decide why Hippolyta wants to marry Theseus, we need to remember that weddings at the end of Shakespeare's comedies were intended to solve any and all problems that arose between a couple during the play. We can assume then that, no matter why Hippolyta wanted to marry Theseus, they lived happily ever after, which is what really matters.