Many hadiths can be found in Sunni references [some of those references being the Sihah Sittah, which are the most authentic books of the Sunni school of thought] that say some verses of the Quran have been omitted, namely the verse of stoning. Nevertheless, although these hadiths exist in their sources, and similar hadiths can also be found in Shia sources as well, even if we accept them, both schools of thought believe that acting according to the Quran we have today brings guidance and salvation and that these slight alterations have no effect on its meaning and similar wording can be found in other verses of the Quran or Islamic tradition.
First off, we would like to say just because there are hadiths in Sunni references that confirm the alteration of the Quran that is in no way any reason to say this is one of the beliefs of the Sunni school of thought. Having made this point first, one can categorize the hadiths that both Shia and Sunni references have narrated on this issue into different categories; some of them actually being explanation, not alteration which have to be separately discussed. The only reason we will address your question is because unfortunately today, some of our Sunni brothers, disregarding the main principle of Muslim unity, falsely assert and propagate that the Shia believe in another Quran and it is only the Sunnis who defend the current Quran and respect it. This matter has caused conflict in the Islamic society and aroused doubt amongst Muslims!
One of the doubts widely spread by these individuals is that the Shia believe in the alteration of some Quranic verses, backing their false claims with some hadiths that can be found in Shia references.
This matter can be answered and solved in two ways:
1- By learning what Shia scholars' viewpoints are regarding the alteration of the Quran; this answer apparently doesn’t have much to do with your question in particular and has been addressed in its proper place; most Shia scholars reject the theory of the alteration of the Quran and dismiss the hadiths that confirm it.
2- By asking our Sunni brothers the same question; are their books and hadith references free of any hadiths that confirm this subject? This is the thing that you are after in your inquiry as well.
The answer to this question is that just because Shia scholars don’t accuse other schools of thought of believing in the alteration of the Quran, doesn’t mean that nothing can be found in their sources that doesn’t confirm this false belief. We will quote five hadiths from Sahih Bukhari; the most authentic reference of the Sunnis which they have named “the sister of the Quran”, yet we don’t encourage any further discussion with them regarding this subject, because it will lead to dispute. If the person you are discussing with is fair, even one of the hadiths we mention will be enough to convince him to stop accusing the Shias of being the only ones with this belief. Now the hadiths:
1- The second khalifah says: “If it wasn’t for me fearing that the people would say that Umar has altered the Quran, I would personally add the verse of the stoning punishment [for the adulterer] to the Quran.”
2- It has been reported that the second khalifah went up the pulpit and after mentioning a few things, he said: “And Allah revealed the Quran unto his messenger, one of its verses being the verse of the stoning punishment and we used to recite this verse, pondering its meaning and memorizing it; it was because of this verse that the prophet would stone the adulterer and we followed his footsteps after him! I fear that after a period of time some will say that no such verse ever existed in the Quran, resulting in Allah’s law not being followed.” He went on to say: “[In addition to the verse of stoning] One of the verses that we would recite during the prophet’s time that isn't recited today is the verse that says: “ان لا ترغبوا عن آبائکم فانه کفر بکم ان ترغبوا عن آبائکم”.
What is interesting is that in some books of our Sunni brothers, it has been said that the verse of stoning was lost because the verse was written on a piece of paper and was kept in the house of Aisha the wife of the prophet, and [since her sheep hadn’t found any food to eat] Lady Aisha’s sheep had devoured the paper!
3- It has been said in another part of this book that: “A verse regarding the martyrs of the incident of “Bi’r Ma’unah” was revealed and we [the second khalifah] would recite it: “ان بلغوا قومنا ان قد لقینا ربنا فرضی عنا و ارضانا” [meaning: “Inform our people that we met our lord and He is happy with us and has made us happy as well”]. After a while this verse was nullified.”
4- I [narrator] heard Umar ibn Khattab saying: “One day I saw Hisham ibn Hakam reciting surah Furqan in a way other than I would recite, although I had learned the surah from the prophet himself. Because of this, I was enraged and was about to harm him, but I waited for him to get moving first. I wound him up in his clothing and took him just like that to the prophet and told him that he was reciting the surah in a way other than what the prophet had taught me. The prophet told me to let him go and asked him to recite the surah. He recited it. The prophet said that he recited it the exact way it was revealed. He then asked me to recite the surah as well. I also recited it. The prophet said that I had also recited it exactly the way it was revealed. He [the prophet] said that the Quran has been revealed in seven ways, and that we should recite it as much as we can.
5- Ibn Abbas has been reported in Sahih Bukhari narrating: “I heard the prophet reciting this excerpt: “لو ان لابن آدم مثل واد مالا لاحب ان له الیه مثله و لا یملا عین ابن آدم الا التراب و یتوب الله علی من تاب” [If man were to have a field full of wealth, he would still desire double that amount and it is only soil that can suppress man’s greed, and Allah accepts the repentance of those who repent]. Ibn Abbas says: “I don’t know if this excerpt the prophet was reciting was part of the Quran or not?”
The five hadiths mentioned above come from the Sunnis most authentic reference. There are hundreds of other hadiths like these in their other books.
Some Sunni scholars have become aware of the fact that there are many hadiths in their books that directly speak of alteration in the Quran and have tried to fix the problem by saying that these hadiths are speaking of naskh [abrogation] in verses or rulings, thus replacing the word “alteration” with “abrogation”. But our question is that for example, in the third hadith mentioned above, why does the verse have to be nullified if there is another verse with the same theme “ارجعی الی ربک راضیة مرضیة” [if it was to be nullified, both had to be nullified because both are speaking of the same thing]. Isn't this exactly alteration itself?! Can't the second khalifah’s belief about the verse of stoning being omitted while its ruling still exists in Islamic law, and him wanting to add the verse back to the Quran, be considered the second khalifah’s belief on the alteration of the Quran?!
Aren’t these hadiths familiar to those used to falsely and unfairly accuse the Shia of believing in the alteration of the Quran?! How can one justify such a paradox?!
To sum it all up, hadiths can be found in both Sunni and Shia sources that confirm the concept of the alteration of the Quran, yet in both schools of thought, it is an accepted fact that acting according to the Qurans that are common and can be found in the homes of both Shias and Sunnis and differ in no way is the way to guidance and salvation. This fact should contribute to the unity of Muslims and shouldn’t be used against them! Debates on this subject should only be theoretical ones, not political or ones that have to do with contrasting between sects.
In closing, we would like to draw your attention to two Shia and Sunni hadiths regarding this final issue:
1- Sufyan ibn Samt narrates that he asked Imam Sadeq (as) about the differences in recitation of the Quran. He said to recite the Quran as we have been taught [and like everyone else].
2- Ibn Masoud, one of the prophet’s (pbuh) companions says: “I have heard the Quran being recited from different reciters and [despite their differences] they were all similar and of the same meaning. Therefore, refrain from disputing about this issue with each other. Truly, some of the differences that can be found are like when we use different words like “هلم” “تعال”and “اقبل” with the same meaning [they all convey the same meaning].
The same goes for synonyms in all languages.
Therefore, we must say that according to most Islamic scholars, no verses have been added to the Quran nor omitted, and if sometimes some individuals from either sect believe that some alteration has occurred, it in no way affects the authenticity of the Quran in its entirety and the belief can't be related to the school of thought as a whole.
 The first answer that we give is one without taking the other side of the argument’s viewpoint into consideration, while the second takes it into consideration.
 Most Shia tafsirs have a separate chapter for this specific subject, you can refer to the following tafsirs to get a glimpse:
1- Allamah Tabatabai, Al-Muzan fi Tafsir Al-Quran, vol.12, pg. 104.
2- Ayatullah Khui, Al-Bayan fi Tafsir Al-Quran, pg.195.
3- Tafsir Nemouneh, vol.11, pg. 18.
 Sahih Bukhari, vol.8, pg.113.
 Ibid, vol.8, pg.26.
 Ibn Athir, Al-Nihayah fi Gharibil-Hadith, vol.2.
 Sahih Bukhari, vol.3, pp.204-208; vol.5, pg.44.
 Ibid, vol.3, pg.90.
 Ibid, vol.7, pg. 175.
 For example, Ayatullah Khui in pages 202-205 of his tafsir, Al-Bayan, after mentioning the viewpoint of Shia scholars on the alteration of the Quran, lists twelve hadiths that can be found in Sunni references that confirm the concept.
 Muhammad ibn Yaqub Kuleini, Al-Kafi, vol.2, pg. 631, hadith 15.
 Beyhaqi, Sunan Kubra, vol.2, pg.385.