To what extent does Desdemona's behavior lead to her tragic end in the play Othello?

Desdemona becomes an innocent victim of Iago's malicious manipulation. Since the devious and vengeful ancient knew much about her nature, he could easily target what he believed were weaknesses that he could exploit. He states at one point:

...For 'tis most easy
The inclining Desdemona to subdue
In any honest suit:

Iago knows that Desdemona would help anyone if she could. At this particular point, Cassio had been dismissed by Othello and Iago had advised the distraught ex-lieutenant to approach Desdemona and ask her to speak to her husband on his behalf. Iago told him that since Desdemona had so much influence on her husband, he would more than likely listen to her.

Iago had plotted to use Cassio's pleas to Desdemona to spur Othello's jealousy. He would tell him that his wife's constant request regarding Cassio was because she wished to satisfy her lust for the young Florentine. The good-natured Desdemona falls easily into Iago's trap. When Cassio approaches her with his request, she says:

Be thou assured, good Cassio, I will do
All my abilities in thy behalf.

She guarantees that her appeal on his behalf will be successful:

O, that's an honest fellow. Do not doubt, Cassio,
But I will have my lord and you again
As friendly as you were.

I know't; I thank you. You do love my lord:
You have known him long; and be you well assured
He shall in strangeness stand no further off
Than in a polite distance.

When Othello and Iago approach, Cassio slips away, prompting Iago to make the following remark:

Ha! I like not that.

When Othello wishes to know the reason for his retort, Iago acts as if he had not said anything inappropriate, making Othello even more suspicious. When Othello asks whether it is Cassio he is speaking about, he says:

Cassio, my lord! No, sure, I cannot think it,
That he would steal away so guilty-like,
Seeing you coming.

This makes the general even more suspicious and when Desdemona does approach him and asks about Cassio, he becomes quite irritated with her. She tells him:

How now, my lord!
I have been talking with a suitor here,
A man that languishes in your displeasure.

Desdemona's word choice actually adds fuel to the fire. Calling Cassio a suitor would later prove to have been an inappropriate term. She then requests that Othello give Cassio a hearing, but he says that he does not have the time. Unknowingly, since she thinks that she is doing Cassio a favor, Desdemona's repeated nagging about the matter irritates Othello even further and would eventually make it easy for Iago to convince him that the two are, indeed, lovers. She is unwittingly digging her own grave.

Desdemona's carelessness with the handkerchief Othello gave her also leads to her being implicated later. When she lets the handkerchief fall, she makes no attempt to recover it, giving Emilia the opportunity to take it and later give it to Iago. When Othello later asks for it, she can only say that she has lost it.

The handkerchief becomes ocular proof for Othello in proving her betrayal later, for Iago takes the handkerchief and places it in Cassio's rooms, where he finds it and later asks Bianca to remove the embroidery, an act witnessed by Othello. He immediately believes that Desdemona gave his most precious gift to her lover.

Throughout the period that Othello suspects her of an affair with Cassio, Desdemona does not challenge her husband enough to present evidence to support his accusations. She is almost apathetic about it. She only denies his accusation that she is a prostitute:

No, as I am a Christian:
If to preserve this vessel for my lord
From any other foul unlawful touch
Be not to be a strumpet, I am none.

When he smacks her in public, she does not confront him about his actions and is rather accepting, almost servile. She says that she would not stay to offend him and walks away.

Another aspect which one might consider is Desdemona's easy acquiescence to her husband's threat that he is going to kill her. She does not cry out for help nor make any attempt to escape. She almost willingly accepts that she has to die. She only asks the Lord to have mercy on her and again denies having an affair.

And have you mercy too! I never did
Offend you in my life; never loved Cassio
But with such general warranty of heaven
As I might love: I never gave him token.

Othello then strangles or suffocates her, and she later dies.