Desdemona is light and good, almost a Christ figure at the end. She is the one character that Iago cannot corrupt. Desdemona tells Emilia in Act 4 that Othello's unkindness may take her life but it will never "taint her love" for him. These words prove to be true at the end of the play when Othello does indeed take Desdemona's life. Desdemona dies still loving Othello. Her last words are "Commend me to my kind lord," even as she tries to absolve him from blame, claiming that she herself took her own life.
Othello has to choose between good (Desdemona) and evil (Iago). A good and honorable man, Othello is convinced that Desdemona is evil and that Iago is good. In Act 3, Othello severs his bond with Desdemona and in almost a parody of a wedding scene pledges his loyalty and love to Iago, swearing that he take revenge on Desdemona and Cassio.
In this way, Desdemona contributes to the tragedy. Othello's wrong choice of Iago over Desdemona is his downfall. All falling acting results from this decision.
But perhaps you were asking if Desdemona is in some way responsible for the tragedy. Some would say her innocence and blindness to Othello's changing loyalties contribute to the tragedy. But she is hardly to be faulted in her love for Othello and her inability to see him other than the honorable soldier who courted her and won her love. You can see her innocence when Othello tells Desdemona that her hand is hot and moist--a double entendre in which he is suggesting that Desdemona is promiscuous. Desdemona responds with "It was the hand that gave my heart away." She does not understand his coarse language. Another example of her innocence and naivete is when she asks Emilia if there are some women who do cheat on their husbands. Emilia responds in the affirmative. Desdemona replies that she would not cheat on Othello for the whole world.
I hope these examples help.
Desdemona plays at least one interesting part in the events that enrage Othello to the point of committing murder. She lies about where the handkerchief is. She loses it, bemoans its loss to Emilia, and then, when Othello asks to see it (III, iv), she says, "I have it not about me," which of course is the truth, for it is lost. But later in the scene:
Is't lost? Is't gone? Speak, is it out o'the way?
It is not lost, but what an if'it were?
I say it is not lost.
Fetch't, let me see it.
Why, so I can sir, but I will not now...
And so, by lying about the fact that the handkerchief is lost, Desdemona adds to Othello's suspicion (since he will, in a later scene, see the handkerchief returned to Cassio by Bianca) and ultimately to her own demise.
Some might argue that Desdemona also shows a possibility of deceitful behaviour when she elopes in the opening of the play with Othello. It would have been highly improper and presumptuous for Desdemona to marry (from her station in society) without first obtaining her father's blessing and permission. This, one could argue, makes her open to question later in the play. If she made a move for love behind her father's back, mightn't she also do so behind Othello's back? It does potentially leave her behaviour open to question and is worth considering.
However, it is the interesting part that the handkerchief plays in Othello, and even Desdemona's own part in the events surrounding it, that push Othello over the edge and lead to the play's tragic ending.