In Hamlet act III scene 2, which of Horatio's qualities does Hamlet admire?
Horatio is Hamlet's closest friend, and in III.ii, the audience can see why, because Hamlet describes the best qualities he sees in Horatio.
First, Hamlet admires that Horatio doesn't allow himself to be broken down by bad fortune. Even though suffering happens to everyone, and Horatio has experienced bad fortune as we all do, he accepts both good and bad fortune without allowing himself to experience extreme, unbridled emotion.
[T]hou hast been
As one, in suff'ring all, that suffers nothing;
A man that Fortune's buffets and rewards
Hast ta'en with equal thanks [...]
Hamlet sees Horatio's calm and steadfastness as signs of good judgment and as a kind of resistance against fate's downturns.
and blest are those
Whose blood and judgment are so well commeddled
That they are not a pipe for Fortune's finger
To sound what stop she please.
This kind of man, this Horatio type who remains even-keeled and always rules himself by reason, rather than passion, is the ideal (according to Hamlet). This rational, loyal, steady man is the kind of friend that Hamlet would allow closest to his heart.
Give me that man
That is not passion's slave, and I will wear him
In my heart's core, ay, in my heart of heart,
As I do thee.
This is a great section, because earlier in the very same scene (III.ii) Hamlet instructs the actors to behave on stage the way Horatio behaves in real life:
in the very torrent, tempest, and (as I may say)
whirlwind of your passion, you must acquire and beget a
temperance that may give it smoothness.
Clearly, the exercise and control of passion is at the very core of how Hamlet sees human nature.
It's worth noting that elsewhere Hamlet accuses his uncle and his mother of being too passionate, and Polonius is concerned that Hamlet's madness stems from passion (in II.i, Polonius says that passion "leads the will to desperate undertakings"). Passion is a dangerous but valuable weapon throughout Hamlet--it is sometimes a necessary spur to action, but it must always be under rational control.