What are some metaphors in Othello?

A metaphor is a comparison that does not use the words "like" or "as."
In act 1, scene 1, Iago tries to incite Brabantio to fury over the elopement of Othello and Desdemona by telling him,

an old black ram is tupping your white ewe

In this instance, Iago is comparing the Othello to a black ram and Desdemona to a white female sheep. The animal metaphors are Iago's way of trying to make the union between the newlyweds seem sordid and bestial.
By act 4, scene 2, Othello has been worked into a frenzy, through Iago's manipulations, into thinking Desdemona has been sleeping with Cassio. He uses heightened language that reflects his emotional distress as he addresses Desdemona. He likens her to a weed, saying, "O thou weed." He then likens her white skin to the light paper in a book and her body to a "goodly book," asking if such pure paper (Desdemona's flesh) were made to become a whore:

Was this fair paper, this most goodly book,
Made to write “whore” upon?

In act 5, scene 2, Emilia is very angry that Othello has killed Desdemona. Emila says,


Oh, the more angel she,
And you the blacker devil!

Here, she uses a metaphor to compare Desdemona to an angel and another one to compare Othello to the devil, playing on traditional (and racist) notions of angels as wearing white and devils as black, again a reference to race as well as Emilia's opinion of their respective characters.

In act I, scene 1, Iago tells Roderigo to yell with great abandon at Desdemona's father's house to waken him. He says, "Do, with like timorous accent and dire yell/ As when, by night and negligence, the fire/ Is spied in populous cities." Using a metaphor, Iago compares the yell Roderigo is supposed to make to the yell people make to warn others of fire in cities. In other words, Roderigo is supposed to make a very loud and powerful yell.
Later, in act II, scene I, Iago, describing women, says to Emilia, "You are pictures out of door, bells in your parlors, wild-cats in your kitchens, saints in your injuries, devils being offended, players in your housewifery, and housewives in your beds." In this speech, Iago uses a series of metaphors, or comparisons. He likens women to pictures (or pretty compositions) when they are outside and to bells that make a lot of noise inside. He compares women to wild cats when in their kitchens, to saints when they are injured, and to devils when they are offended. When they are doing chores, they are "players" who do not take things seriously, and they are tarts in bed. This series of metaphors describing women is far from complimentary and could be considered misogynistic. 
In act II, scene 3, Othello says to Desdemona, "The purchase made, the fruits are to ensue: That profit’s yet to come ’tween me and you." In this speech, Othello compares his marriage to a sale. Now that he has purchased Desdemona, he can enjoy what he has purchased, which means his ability to sleep with Desdemona. He clearly treats her like goods that he has bought and can treat any way he wishes.