What are some quotes that demonstrate Iago's manipulations in Othello?

Firstly, the fact that Iago declares his intention to harm Othello when he speaks to Roderigo, is a good quote:

I follow him to serve my turn upon him

Iago clearly and unambiguously says here that he only shows obedience to Othello to fool him into believing that he is being loyal and servile so that he may plot his downfall - true to the expression 'Keep your enemies closer.'

In the same speech he tells Roderigo:

... Others there are
Who, trimm'd in forms and visages of duty,
Keep yet their hearts attending on themselves,
And, throwing but shows of service on their lords,
Do well thrive by them and when they have lined
their coats
Do themselves homage: these fellows have some soul;
And such a one do I profess myself. 

It is obvious in these lines that Iago has much admiration for the type of servant who only obeys his master out of show and not because of genuine respect or duty. His sole purpose is to serve his own needs - they do homage to themselves. Such persons show spirit and Iago perceives himself to be the same. A confession of his devious and pernicious nature.

Iago has planned to rouse Brabantio, the beautiful and chaste Desdemona's father, to inform him that Othello had kidnapped her. The plan is to upset Brabantio to such an extent that he would take action against Othello. When the two arrive at his house, Iago shouts that there were thieves around. When Brabantio wakes and enquires what all the noise is about, Iago declares:

Zounds, sir, you're robb'd; for shame, put on
your gown;
Your heart is burst, you have lost half your soul;
Even now, now, very now, an old black ram
Is topping your white ewe. Arise, arise;
Awake the snorting citizens with the bell,
Or else the devil will make a grandsire of you:
Arise, I say.

Iago uses the most disgusting animal metaphors to inform Brabantio that his daughter is being sexually abused. He cleverly refrains from mentioning the so-called abuser by name, but makes indirect references to Othello. He is incessant and continues using these images to further shock Brabantio, who later seeks out the duke and demands Othello's arrest.

Iago later maliciously informs Othello about how badly Brabantio had spoken about him:

Nay, but he prated,
And spoke such scurvy and provoking terms
Against your honour
That, with the little godliness I have,
I did full hard forbear him.

He tells Othello that Brabantio criticized him at length and used such shocking and provocative references that he, Iago found it difficult to restrain himself from lashing out at Brabantio. Iago has now manipulated both men and ruined, in a very short time, the good relationship (though superficial) that existed between the two.

Iago also masterfully manipulates the foolish Roderigo to do his bidding by dangling the fact that he would help him pursue Desdemona's affections and win her over in front of him like a carrot. He tells Roderigo:

Thou art sure of me:--go, make money:--I have told
thee often, and I re-tell thee again and again, I
hate the Moor: my cause is hearted; thine hath no
less reason. Let us be conjunctive in our revenge
against him: if thou canst cuckold him, thou dost
thyself a pleasure, me a sport.

He tells Roderigo that they should work together against Othello. In this venture, both will achieve what they want - he revenge and Roderigo Desdemona.

There are many other examples of Iago's manipulations but the one which stands out particularly since it finally convinces Othello of Desdemona's 'infidelity', is Cassio's speech with Bianca. Iago had planted Desdemona's handkerchief in Cassio's room and he is now speaking to him. Othello is in hiding, eavesdropping. Cassio speaks:

She was here even now; she haunts me in every place.
I was the other day talking on the sea-bank with
certain Venetians; and thither comes the bauble,
and, by this hand, she falls me thus about my neck--

Othello thinks that Cassio is speaking about his wife, but he is speaking about Bianca. She arrives later and angrily confronts Cassio:

Let the devil and his dam haunt you! What did you
mean by that same handkerchief you gave me even now?
I was a fine fool to take it. I must take out the
work?--A likely piece of work, that you should find
it in your chamber, and not know who left it there!
This is some minx's token, and I must take out the
work? There; give it your hobby-horse: wheresoever
you had it, I'll take out no work on't.

When Othello sees the handkerchief, he is fully convinced that he has been cuckolded. His mind is made up and he sets in motion the tragic events which transpire later.