What does the character Othello lose in the play of the same name?

Firstly, Othello loses Iago's loyalty, for his ancient turns against him when he does not appoint him in the position of lieutenant. Iago is deeply embittered and swears revenge. He tells Roderigo that he will act as if he is still loyal to the general in order to deceive him and wait for the ideal opportunity to strike. He informs Roderigo in Act 1, scene 1:

...I follow him to serve my turn upon him:...

...Were I the Moor, I would not be Iago:
In following him, I follow but myself;
Heaven is my judge, not I for love and duty,
But seeming so, for my peculiar end:... 

It is also obvious that Othello loses respect for his new bride's father, Brabantio, for he displays his racism and prejudice towards the general when he accuses Othello of abducting his daughter, using witchcraft and plying her with potions in order to abuse her. He unquestioningly believes Iago and Roderigo's lies and assumes that Othello is guilty. His remarks when he confronts Othello in Act 1, scene 2, also indicate his bigotry.  

O thou foul thief, where hast thou stow'd my daughter?
Damn'd as thou art, thou hast enchanted her;
For I'll refer me to all things of sense,
If she in chains of magic were not bound,...

...Run from her guardage to the sooty bosom
Of such a thing as thou, to fear, not to delight.
Judge me the world, if 'tis not gross in sense
That thou hast practised on her with foul charms,
Abused her delicate youth with drugs or minerals
That weaken motion: I'll have't disputed on;...

Clearly, Othello cannot respect him for such blatant bias.

When Iago manipulates Othello and preys on his weaknesses, the general also loses his self-control and rationality. He becomes careless an irrational because of jealousy. He believes Iago's lies about Desdemona's deceit and in Act 4, scene 1, he calls her a devil and strikes her in public, with Lodovico witnessing his physical and verbal abuse. In this regard, then, he also loses his trust in her since he believes she and Cassio are cuckolding him.

OTHELLO
[Striking her] Devil!

DESDEMONAI have not deserved this.

LODOVICO
My lord, this would not be believed in Venice,
Though I should swear I saw't: 'tis very much:
Make her amends; she weeps.

OTHELLO
O devil, devil!
If that the earth could teem with woman's tears,
Each drop she falls would prove a crocodile.
Out of my sight!

On a literal level, Othello also believes that he has lost a precious possession, a handkerchief from his mother which he gave to Desdemona as a gift. When he asks her for it, she has no idea where it is. Unbeknownst to her, Emilia had picked up the napkin and gave it to Iago who would use it as ocular proof later as evidence of Desdemona and Cassio's supposed illicit affair. In Act 3, scene 4, Othello demands to know where the napkin is and when Desdemona tells him that she does not know, he says:

That is a fault.
That handkerchief
Did an Egyptian to my mother give;
She was a charmer, and could almost read
The thoughts of people: she told her, while
she kept it,
'Twould make her amiable and subdue my father
Entirely to her love, but if she lost it
Or made gift of it, my father's eye
Should hold her loathed and his spirits should hunt
After new fancies: she, dying, gave it me;
And bid me, when my fate would have me wive,
To give it her. I did so: and take heed on't;
Make it a darling like your precious eye;
To lose't or give't away were such perdition
As nothing else could match.

Othello is so overwhelmed by his jealousy and Desdemona's apparent betrayal that he decides to murder her. He suffocates her in bed and thus also loses a dear and loving wife, who had been loyal to him throughout.

In the end he also loses his own life for he is overcome by remorse when he discovers Iago's malicious deception and that he had been played like a puppet by his vindictive ancient. He decides to die with honor rather than live with the unalterable crime on his conscience. Before he commits suicide, he admits to the grievous error that he had committed and that he had lost something priceless (Desdemona). In his final words at the end of Act 5, scene 2, he declares, in part:

Set you down this;
And say besides, that in Aleppo once,
Where a malignant and a turban'd Turk
Beat a Venetian and traduced the state,
I took by the throat the circumcised dog,
And smote him, thus.

He then stabs himself and dies.