The importance of fulfilling the rights of parents (father and mother) has been recognized by the Quran to be so high that in several verses, it has been demanded immediately after forbidding shirk (polytheism) and has been known as one of the most virtuous acts in the ahadith. A few examples of the rights mentioned in the Quran and tradition are as follows:
1. Speaking politely with parents and being humble with them
2. Praying to God to bestow His mercy on them
3. Obeying them in everything except haram
The topic of parents’ rights has been given a lot of attention in the Quran and ahadith; we will expand on this subject in the following segments:
Importance of parents’ rights in the Holy Quran
The Quran has given so much importance to the point where, in several verses, it has promoted to do parents good immediately after forbidding shirk (polytheism). For example in the covenant made with Bani Israel (the children of Israel), he says: “And (remember) when we made a covenant with the children of Israel: You shall not serve any but Allah and (you shall do) good to (your) parents”.  It is clear that making a covenant to be kind with parents implies how important it is. In another part of the Quran, using the word “ و قضی ربک ” meaning “the lord has decreed” and again straight after mentioning shirk, He demands to do good to parents.  This issue can be witnessed in several verses such as Surah An-Nisa’/36, Surah Al-Anaam/151, Surah Al-Ankabut/8, Surah Luqman and Al-Ahqaf/15.
On top of this, Allah has emphasized on the significance of this topic by reminding us how the Awliya’ullah (Friends of Allah) and the prophets were good to their parents; for example in the chapter of Maryam, in addition to mentioning the noble traits instilled in Prophet Yahya (A.S.) he states that he treated his parents very well. 
Importance of parent’s rights in traditions
In a hadith, Imam Sadiq’s (A.S.) reply to the question “which action is the highest and greatest action” was “on-time (not delayed) prayer, doing your parents good and jihad”. By mentioning the act of doing good to parents after on-time prayer and before jihad we can easily deduce how important it is in the eyes of the imams. In another hadith narrated from Imam Sadeq (A.S.), he considers doing good to parents, whether they are righteous or corrupt, to be one of those duties that which no excuse is accepted for. 
Examples of parent’s rights in the Quran and ahadith
Several examples of rights that parents have over their children have been mentioned, in a concise manner, in the Quran and ahadith. Here, we will take a brief look at a few of them:
A. Speaking politely
In an ayah Allah states: “ If either or both of them reach old age with you, say not to them (so much as) "Ugh" nor chide them, and speak to them a generous word.”  In a hadith, Imam Sadeq (A.S.) says if there was a word that would imply less than what uff (ugh) implies, God would have forbidden that [would have used that word instead of uff]. 
In the rest of the verse mentioned above Allah says: “ And lower unto them (mother and father) the wing of submission through mercy.”  The metaphor of “lowering the wing of submission” in this ayah implies the utmost measure of humbleness.
A hadith has been narrated that Imam Sadiq (A.S.) declares: “The child has three duties towards his parents; continuously being thankful of them, obeying whatever they demand or forbid unless it results in a sin and doing good to them in private and public.” 
In the same verses Allah orders to pray for them also: “An d say: O my Lord! have compassion on them, as they brought me up (when I was) little.” 
In addition to these points, even more detailed examples have been pointed out; like the hadith where Imam Musa al-Kadhim (A.S.) says that the Prophet (S.A.) was asked about the rights the father has over his child and he replied that the child must never call his parents by their first name, walk in front of them or sit before they do, nor give others an excuse to insult them.”  In a verse of the Quran parents have been declared to be the priority for receiving charity, the ayah says: “They ask you as to what they should spend (in charity). Say: Whatever wealth you spend, it must go to the parents and the near of kin”. 
The limit to obeying parents
From the earlier points mentioned, one might get the impression that it is necessary to obey parents regardless of what they say in order to fulfill their rights, but what must be noted is that from the Quran’s perspective this isn’t acceptable in its entirety. From the Quran’s perspective it is only necessary to obey parents when it doesn’t result in disobeying Allah and being deviated from justice and the right path. As Allah says in a verse of the Quran: “Be maintainers of justice as witnesses of Allah, though it may be against your own selves or (your) parents or near relatives”. 
Similar to the above, in a different verse, he has warned us not surrender to the struggle and endeavor of our parents if they – God forbid - intend to make us mushrik (polytheist): “And We have enjoined on man goodness to his parents, and if they contend with you that you should associate (others) with Me, of which you have no knowledge, do not obey them…”.  However the Quran ultimately declares that disobeying one’s parents in committing shirk to Allah doesn’t mean that one can be harsh with them, where it says: “…and keep company with them in this world kindly”. 
In addition to encouraging us to treat our parents in a kind and respectful manner the Quran and ahadith also state that this obligation has been put onto us in exchange for all the struggle and effort they have gone through, especially the mother, to take care of and raise us.  
For more information please see:
Parent’s demands and children’s duties, Question 9455, (Site: 9458).
 “ و قضی ربک ألا تعبدوا إلا إایاه و بالوالدین احسانا... ” (Your Lord has decreed that you shall not worship anyone except Him, and [He has enjoined] kindness to parents) Israa’:23.
 “ و برّا بوالدیه و لم یکن جبارا عصیا ” Maryam:14.
 Sheikh Tusi, Al-Tahdhib, vol. 6, pg. 350, Daar al-Kutub al-Islamiyah, Tehran, 1986.
 Kuleini, Kāfī, vol. 2, pg. 349.
 Majlisi, Muhammad Baqir, Bihar al-Anwar, vol. 75, pg. 236, al-Wafaa’ Insititute, Beirut, Lebanon, 1404 AH.
 Kuleini, Kāfī, vol. 2, pg. 158, Daar al-Kutub al-Islamiyah, Tehran, 1986.
 “ ...کونوا قوامین بالقسط شهداء علی انفسکم او الوالدین و الاقربین... ” Nisaa’:135.
 Luqman:14; Ahqaf:15; Israa’:24.
 Adopted from an article in the website for answering religious questions.