This is a great question. Two acts of betrayal come to mind. First, the most obvious example is the actions of the suitors. Just because Odysseus does not come back, these suitors try to gain the affection of Penelope. Moreover, they take advantage of Odysseus's goods. This is even worse, because Odysseus is the ruler of Ithaca. In other words, he is their king. So, this lack of loyalty is betrayal.
Second, we see another act of betrayal when the men of Odysseus open a bag of winds, which Aelous gave to Odysseus. They open this bag, because of their greed. They believed that the bag was filled with gold and silver and they wanted it. So they opened up the bag only to allow winds to gush forth and throw the ships completely off track. In light of this, we can say that his men did not trust him. So, one can argue that this act is tantamount to an act of betrayal.
You want examples of Betrayal? Look at Aggamemnon's wife, Clytemnestra, who not only took a lover while Aggamemnon was away, but plotted with him to kill Aggamemnon when he came back.
Another example of betrayal would be not the suitors, but the 12 (depending on the version you have) serving women who sleep with the suitors. At least one of these women openly betrayed penelope by revealing her looming trick. They fact that they treat the suitors well is a betrayal of Telemachus (The suitors are eating away his inheritance and plotting to kill him). Thes actions are likewise a betrayal of Odysseus as they are dishonoring odyssues, etc. Also, Melanthius, another of Odyssues' servants actually arms the Suitor against Odysseus, when oddysseus goes postal on everyone.