Depends on what you are doing:
Torah study is greater than the mitzvah of honoring parents. [Megillah 16b]
But in general, you don't have to obey your parents:
-If someone wants to pray in a synagogue where [the congregation] prays with more devotion, and his mother protests, he does not have to listen to his mother. [19th-century Russian rabbi Eisenstadt, Pitchei Teshuva, Yoreh Deah 240:22]
-If the father protests against the son marrying a specific woman that he wishes [to marry], the son does not have to listen to his father. [Rema on Shulchan Aruch Yoreh Deah 240:25] (But if she is not Jewish, or not moral, or not religious, he must listen to his father. [Chaim Hezekiah Medini, 19th-century Jerusalem rabbi, Sdei Chemed, Ma’arechet Caf 147])
-Many rabbis say that the mitzvah to dwell in Israel overrides the obligation to honor parents. Some disagree. [Contemporary rabbi Moshe Lieber, The Fifth Commandment, p 131]
-If a parent asks a son to shave his beard, he need not listen. If a parent tells a child not to speak to a certain person, the child need not obey. [Shulhan Arukh, Yoreh De'ah 240:16; Rabbi Shlomo Zalman Braun, She'arim Metzuyyanim Bahalakhah 143]
However, the Talmud says:
Rabbi Aha ben Yaakov raised his daughter's son, Rabbi Yaakov. When he grew up, [the grandfather] said to him: “Give me some water to drink”. He replied: “I am not your son.” [Sotah 49a]
This implies that, had he been the son, he would have had to obey.
My conclusion from all this: Generally, you must obey your parents when it's a matter that concerns primarily your parents and does not violate commandments, but not when it's a matter that concerns primarily you. There are exceptions. But yes, you must take out the garbage if it's THEIR garbage and you are not studying Torah at that moment. Otherwise you don't.