What do Othello and Desdemona find attractive about one another?

Othello in his address to the duke explains how the two
fell in love.  He sums up his story with these lines:

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She loved me for the dangers I had
passed,

And I loved her that she did pity
them. 

This only is the witchcraft I have
used.

When Othello visited
Brabantio's house, he would tell stories of his adventures.  Desdemona would listen with
such interest and sympathy that the two fell in love.  Desdemona, most likely, was quite
sheltered, and was immediately attracted to the man who committed such heroic deeds. In
turn, Othello delighted in Desdemona's interest and compassion for the dangerous life he
had led.  Shakespeare makes it clear through this speech that Othello and Desdemona's
love was not an infatuation, that it grew over time, and it was based not on looks or
superficialities but rather on personalities and history.  Desdemona is presented as a
mature, sensitive young lady while Othello is portrayed as nothing short of a
hero. 

Later Desdemona
declares,

I
saw Othello's visage in his mind,

And to his honors and his
valiant parts

Did I my soul and fortunes
consecrate. 

Desdemona loves
Othello not for his looks but for the way he thinks.  Othello loves Desdemona because
she exhibits the traits of the ideal woman of that time period:  submissive, obedient,
faithful, quietly spoken, accomplished in dancing, singing, and sewing. But Othello
senses the basic goodness of Desdemona as he does initially with Cassio.  Othello's
instinctive judgments of those around him are probably sound:  he did choose Cassio over
Iago for his lieutenant.  It is only when he begins to listen to Iago's insinuations
that he begins to doubt himself and his own judgments of those he
loves.