Are "dream catchers" considered to be avodah zarah?
Dreamcatcher: a small hoop containing a horsehair mesh, or a similar construction of string or yarn, decorated with feathers and beads, believed to give its owner good dreams. Dreamcatchers were originally made by American Indians.
I have seen them around. Periodically, I even see the in the homes of shomer Shabbos people.
If you are not worshiping it (or possibly using it as a conduit of worshiping G-d), then it is not Avodah Zarah. After all, it is not a statue or figure or anything of the like.
The real issue involved would be Nichush. The Rambam writes in the Yad Hachazakah, Hilchot Avodah Zarah V'Chukot HaGoyim, 11:4:
אֵין מְנַחֲשִׁין כְּעַכּוּ'ם שֶׁנֶּאֱמַר "לֹא תְנַחֲשׁוּ". כֵּיצַד הוּא הַנַּחַשׁ. כְּגוֹן אֵלּוּ שֶׁאוֹמְרִים הוֹאִיל וְנָפְלָה פִּתִּי מִפִּי אוֹ נָפַל מַקְלִי מִיָּדִי אֵינִי הוֹלֵךְ לְמָקוֹם פְּלוֹנִי הַיּוֹם שֶׁאִם אֵלֵךְ אֵין חֲפָצַיי נַעֲשִׂים. הוֹאִיל וְעָבַר שׁוּעָל מִימִינִי אֵינִי יוֹצֵא מִפֶּתַח בֵּיתִי הַיּוֹם שֶׁאִם אֵצֵא יִפְגָּעֵנִי אָדָם רַמַּאי. וְכֵן אֵלּוּ שֶׁשּׁוֹמְעִים צִפְצוּף הָעוֹף וְאוֹמְרִים יִהְיֶה כָּךְ וְלֹא יִהְיֶה כָּךְ. טוֹב לַעֲשׂוֹת דָּבָר פְּלוֹנִי וְרַע לַעֲשׂוֹת דָּבָר פְּלוֹנִי. וְכֵן אֵלּוּ שֶׁאוֹמְרִים שְׁחֹט תַּרְנְגוֹל זֶה שֶׁקָּרָא עַרְבִית. שְׁחֹט תַּרְנְגלֶת זוֹ שֶׁקָּרְאָה כְּמוֹ תַּרְנְגוֹל. וְכֵן הַמֵּשִׂים סִימָנִים לְעַצְמוֹ אִם יֶאֱרַע לִי כָּךְ וְכָךְ אֶעֱשֶׂה דָּבָר פְּלוֹנִי וְאִם לֹא יֶאֱרַע לִי לֹא אֶעֱשֶׂה, כֶּאֱלִיעֶזֶר עֶבֶד אַבְרָהָם. וְכֵן כָּל כַּיּוֹצֵא בַּדְּבָרִים הָאֵלּוּ הַכּל אָסוּר. וְכָל הָעוֹשֶׂה מַעֲשֶׂה מִפְּנֵי דָּבָר מִדְּבָרִים אֵלּוּ לוֹקֶה:
(Chabad.org translation) It is forbidden to practice soothsaying as idolaters do, as [Leviticus 19:26] states: "Do not act as a soothsayer."
What is meant by a soothsayer? For example, those who say: Since my piece of bread fell out of my mouth, or my staff fell from my hand, I will not travel to this place today, since if I were to go I would not be able to accomplish my desires.
Since a fox passed on my right side, I will not go out of my door today, since if I were to go out I would meet a deceiver.
Similarly, [this category includes] those who hear the chirping of a bird and say: This will happen or this will not happen; it is beneficial to do this or it is detrimental to do this. [Also, it includes] those who say: Slaughter this rooster that crowed like a raven; slaughter this hen that crowed like a rooster.
Similarly, a person who sets up omens for himself; e.g., if this and this happens, I will do this. If it will not happen, I will not do it, as Eliezer, the servant of Abraham did, and the things of the like - all this is forbidden. Anyone who does one of these things because of such omens is [liable for] lashes.
Indeed, a form of this passage is found in the Shulchan Aruch, Yoreh De'ah, 179:3, and it rules this Assur.
Thus, while the problem is not Avodah Zarah, there is still a major Halachic problem.
