http://www.usc.edu/dept/MSA/fundamentals/hadithsunnah/bukhari/011.sbt.html#001.011.638Volume 1, Book 11, Number 638:
Narrated Abu Sa'id Al-Khudri:
A cloud came and it rained till the roof started leaking and in those days the roof used to be of the branches of date-palms. Iqama was pronounced and I saw Allah's Apostles prostrating in water and mud and even I saw the mark of mud on his forehead.
http://www.usc.edu/dept/MSA/fundamentals/hadithsunnah/bukhari/012.sbt.html#001.012.775Volume 1, Book 12, Number 777:
Narrated Abu Salama:
Once I went to Abu- Sa'id Al-Khudri and asked him, "Won't you come with us to the date-palm trees to have a talk?" So Abu Said went out and I asked him, "Tell me what you heard from the Prophet about the Night of Qadr." Abu Said replied, "Once Allah's Apostle performed I'tikaf (seclusion) on the first ten days of the month of Ramadan and we did the same with him. Gabriel came to him and said, 'The night you are looking for is ahead of you.' So the Prophet performed the I'tikaf in the middle (second) ten days of the month of Ramadan and we too performed I'tikaf with him. Gabriel came to him and said, 'The night which you are looking for is ahead of you.' In the morning of the 20th of Ramadan the Prophet delivered a sermon saying, 'Whoever has performed I'tikaf with me should continue it. I have been shown the Night of "Qadr", but have forgotten its date, but it is in the odd nights of the last ten nights. I saw in my dream that I was prostrating in mud and water.' In those days the roof of the mosque was made of branches of date-palm trees. At that time the sky was clear and no cloud was visible, but suddenly a cloud came and it rained. The Prophet led us in the prayer and
I saw the traces of mud on the forehead and on the nose of Allah's Apostle. So it was the confirmation of that dream."
There are MANY such ahadith, in the 'sahih' bukhari, but insha Allah the above should suffice.
http://www.usc.edu/dept/MSA/fundamentals/hadithsunnah/muslim/004.smt.html#004.0958Book 004, Number 1296:
Anas b. Malik reported: We used to say (the noonprayer) with the Messenger of Allah (may peace be upon him) in the intense heat, but when someone amongst us found it hard to place his forehead on the ground, he spread his cloth and prostrated on it.
**** Although shias don't believe in these particular hadith, it's to prove that even in sunni literature, ONLY when someone found it extremely hard (in intense heat) did he spread his own cloth, otherwise he prostrated on the ground.
Even when it was extremely hot, at times the companions didn't use cloth:
http://www.usc.edu/dept/MSA/fundamentals/hadithsunnah/abudawud/002.sat.html#002.0399Book 2, Number 0399:
Narrated Jabir ibn Abdullah:
I would offer my noon prayer with the Apostle of Allah (peace_be_upon_him) and took a handful of gravels so that they might become cold in my hand and I placed them (before me) so that I may put my forehead on them at the time when I would prostrate. I did this due to the intensity of heat.
http://www.usc.edu/dept/MSA/fundamentals/hadithsunnah/muslim/006.smt.html#006.2627Book 006, Number 2627:
Abu Sa'id al-Khudri (Allah be pleased with him) reported that the Messenger of Allah (may peace be upon him) observed i'tikaf (confined himself for devotion and prayer) in the first ten (days) of Ramadan; he then observed i'tikaf in the middle ten (days) in a Turkish tent with a mat hanging at its door. He (the Holy Prophet) took hold of that mat and placed it in the nook of the tent. He then put his head out and talked with people and they came near him, and he (the Holy Prophet) said: I observed i'tikaf in the first ten (nights and days) in order to seek that night (Lailat-ul-Qadr). I then observed i'tikaf in the middle ten days. Then (an angel) was sent to me and I was told that this (night) is among the last ten (nights). He who among you likes to observe i'tikaf should do so; and the people observed it along with him, and he (the Holy Prophet) said: That (Lailat-ul-Qadr) was shown to me on an odd (night) and I (saw in the dream) that I was prostrating in the morning in clay and water. So in the morning of the twenty-first night when he (the Holy Prophet) got up for dawn (prayer). there was a rainfall and the mosque dripped, and I saw clay and water. When he came out after completing the morning prayer (I saw) that
his forehead and the tip of his nose had (traces) of clay and water, and that was the twenty-first night among the last ten (nights).
***** Again it's demonstrated that the Prophet (s) didn't use a cloth for prostration.
The above should suffice for any Sunni brother/sister seeking the truth with an open and objective mind.
As for the Salafis, even Ibn Taymiyya has said that it's not from the prophet's sunnah or that of the companions to pray on a prayer mat, and that they used to pray on the earth:
http://arabic.islamicweb.com/Books/taimiya.asp?book=381&volume=22&page=163 
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