What are some examples of treachery and loyalty in Shakesepeare's tragedy Othello? Please cite act and scene.

Loyalty and treachery are important themes in
Shakespeare’s Othello from the very opening words of the play. 
Thus, in the very first scene, Roderigo is already accusing Iago of a mild kind of
treachery (or at least disloyalty) by not informing him of Othello’s marriage to 
Desdemona (1.1.1-3).  Iago immediately responds by claiming his loyalty to Roderigo
(1.11.4-6). Iago feels that Othello has been treacherous to him by choosing Michal
Cassio as his [Othello’s] lieutenant rather than Iago himself (1.1.8-17). Iago feels
that he has been loyal to Othello (1.1.28-33) and thus feels all the more that he [Iago]
has been treated treacherously.  In turn, Iago plans to deal treacherously with
Othello:

O,
sir, content you;

I follow him to serve my turn upon him.
(1.1.41-42)

Iago plans to
pretend loyalty to Othello merely to plot revenge: “In following him, I follow but
myself” (1.1.58). Within a few lines, he is already proclaiming to Brabantio that the
latter has been treated treacherously by Othello, who has secretly married Brabantio’s
daughter, Desdemona, without her father’s consent:

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I am one, sir, that comes to tell you your
daughter and the Moor are [now] making the beast with two backs.
(1.1.115-17)

In other words,
Iago claims that not only has Othello been treacherous to Brabantio but that Brabantio’s
own daughter has been disloyal as well.

Later, in the
streets of Venice, Brabantio himself accuses Othello of
treachery:

O
thou foul thief, where hast thou stowed my daughter?

Damn’d
as thou art, thou hast enchanted her . . . .
(1.2.62-63)

Later still, in
the Ventian court, Brabantio once more charges Othello with treachery, claiming that
Desdemona has been

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abus’d, stol’n from me, and
corrupted

By spells and medicines brought on by mountebanks
. . . . (1.3.60-61)

When
Desdemona herself appears before the court, she professes loyalty both to her father and
to her new husband; she denies that she has acted treacherously but instead proclaims
that now her greater loyalty must be to the man she has married rather than to the man
who helped conceive her (1.3.180-89). Brabantio disdainfully accepts what has happened,
but, before leaving the court, warns Othello that Desdemona may someday treat Othello as
treacherously as Brabantio feels he himself has been
treated:

Look
to her, Moor, if thou hast eyes to see;

She has deceived
her father, and may thee.
(1.3.292-93)

Othello responds
to this warning by replying simply, “My life upon her faith!” (1.3.294) – words that
imply his own loyalty toward Desdemona as well as his trust in her loyalty toward him. 
Throughout the entire first act of the play, then, loyalty and treachery are crucial
themes.

Other scenes in which these themes particularly
appear include the following: 2.1.213-312; 2.3.204-49; 3.3.155-278; 3.3.330-480;
4.1.1-212; 42.31-90; 5.1.35-73; 5.2.1-83; 5.2.126-67; and 5.2.283-87.  There are, in
fact, few scenes in the play that fail to at least touch upon the themes of treachery
and loyalty.