1. Al-A'raf (Chapter 7, Verse 206):
"Those who are near to your Lord, disdain not to do Him worship; they celebrate His Praises and to Him they prostrate themselves."
2. Al-Ra'd (chapter 13, Verse 15):
"Whatever beings there are in the heavens and the earth do prostrate themselves to Allah with goodwill or inspite of themselves: so do their shadows in the mornings and evenings."
3. Al-Nahl (Chapter 16, Verses 49-50):
"And unto Allah prostrate all that is in heavens and on earth, whether moving living creatures or the angels: for none are arrogant (before their Lord). They all fear their Lord High above them, and they do all that they are commanded."
4. Al-Israa' (Chapter 17, Verses 107-109):
"Say: 'Whether you believe in it or not' It is true that these who were given knowledge beforehand, when it is recited to them fall down on their faces in humble prostration and they say: 'Glory to our Lord. Truly the promise of our Lord has been fulfilled.' They fall down on their faces in tears, and it increases their earnest humility."
5. Maryam (Chapter 19, Verse 58):
"Those were some of the prophets on whom Allah bestowed His Grace of the posterity of Adam, and of those whom We carried (in the Ark) with Noah, and of the posterity of Ibrahim and Israel - of those whom We guided and chose; whenever the Signs of Allah Most Gracious were rehearsed to them, they would fall down in prostrate adoration and in tears."
6. Al-Hajj (Chapter 22, Verse 18):
"Don't you see that to Allah bow down in worship all things that are in the heavens and on earth - the sun, the moon, the stars, the mountains, the trees, the animals, and a great number among mankind? But a great number are also such as are fit for punishment: and such as Allah shall disgrace, none can raise to honor: for Allah carried out all that He wills."
7. Al-Hajj (chapter 22, verse 77):
"O you who believe! Bow down, prostrate yourselves, and worship your Lord; and do good so that you may prosper."
8. Al-Furqan (Chapter 25, Verse 60):
"When it is said to them: 'Prostrate yourselves to the Most Gracious', they say: 'What is the Most Gracious? Shall we prostrate ourselves to that which you command us?' And it increases their flight from the Truth."
9. Al-Naml (Chapter 27, Verses 2-27):
"I found there a woman ruling over them provided with every requisite; and she has a magnificent throne. I found her and her people prostrating themselves to the sun away from Allah; the Devil has made their deeds seem pleasing to their eyes, and has kept them away from the Path - so they receive no guidance - that they should not prostrate themselves to Allah, Who brings to light what is hidden in the heavens and the earth, and knows what you hide and what you reveal. Allah! there is no god but He! Lard of the Throne Supreme."
10. Al-Sajdah (chapter 32, Verse 15):
"Only those who believe in Our Signs, who, when they are reminded of them (through recitation) fall down in prostration and celebrate the praises of their Lord; nor are they (ever) puffed up with pride."
11. Saad (Chapter 38, Verse 24):
"(Dawood) said: 'He has undoubtedly wronged you in demanding your single ewe to be added to his flock of ewes; truly many are the partners who wrong each other: Not so do those who believe and work deeds of righteousness, and how few are, they?' Dawood then gathered that We had tried him: so he asked forgiveness of his Lord, fell down bowing in prostration and turned to Allah in repentance."
12. Fussilat (Chapter 41, Verses 37-38):
"And among His Signs are the Night and the Day, and the Sun and the Moon. Don't prostrate yourselves to the Sun and the Moon, but prostrate to Allah, who created them if it is Him you wish to worship. If however, they are arrogant, those who are in the presence of your Lord celebrate His praises by night and by day and they never flag."
13. Al-Najm (Chapter 53, Verse 62):
"Do you then wonder at this recital? And will you laugh and not weep, wasting your time in vanities? Rather fall down in prostration to Allah and worship Him (alone)!"
14. Al-lnshiqaq (Chapter 84, Verse 21):
"What then is the matter with them, that they do not believe? And when the Quran is recited to them they fall not prostrate?'
15. Al-'Alaq (Chapter 96, Verse 19):
"Knows he not that Allah does see? Nay. let him beware! If he desist not, We will drag him by the forelock - a lying, sinful forelock! Then let him call for help to his council (of comrades): We will call on the angels of punishment. Nay: had him not. But bow down in prostration and bring yourself the closer (to Allah)."

Taken from here

There is legitimate difference of opinion in this both in Fiqh and in Riwayaat of Quran (For Example Imam Warsh follows the School of Imam Malik in Sajdas). So it is good to be aware of it, as not to fight in Salah

In the book, Al-Tibyaan fi Sajadat Alquran (summarized translation):

The Hanafis: have 14 Sajdas; they do not count the second Sajda of Sura Hajj (#7)

The Malikis: have 11 Sajdas; they do not count the second Sajda of Surah Hajj (#7), the Sajdas of Sura Najm (#13), Inshiqaq(#14) 'Alaq (#15)

The Shafi's: have 14 Sajdas; they do not count the Sajda of Sura Sad (#11)

The Hanbalis: their Mashur is same as Shafi;is. while a weaker opinion counts all of the 15 as Sajdas.

Wallahu Taala Alam.