What are the reasons Othello believes Desdemona might be cheating on him?

Iago starts it all by convincing Roderigo that Desdemona will stray from Othello, as she has already done with Cassio.

Cassio is tricked into asking Desdemona to vouch for him with Othello, which she of course does because she does not know she is being set up.

Othello gets angry because Desdemona is so persistant in her plea for Cassio.

Desdemona drops the handkerchief that Othello gave her on their honeymoon; Emilia knew that her husband had wanted it for something, so she doesn't feel too guilty about taking it. Emilia gives it to Iago, who decides to use the handkerchief for his own devices.

Othello re-enters, and tells Iago that he now doubts his wife; Othello demands "ocular proof" of Desdemona's dishonesty, so Iago sets about making stories up about Cassio talking in his sleep, and says that Cassio has the handkerchief that Othello gave to Desdemona. Iago knows how important this handkerchief is to Othello; it was his first gift to Desdemona, and was given to him by his mother. Othello is incensed to hear that Desdemona would give away something so valuable, and is persuaded by Iago's insinuations and claims to believe that Desdemona is guilty. Othello then swears to have Cassio dead, and to be revenged upon Desdemona for the non-existent affair.

In the end, Othello kills his wife.

Source(s): http://www.gradesaver.com/othello/study-guide/short-summary/