Which verses of the Sama Veda are unique to itself and are NOT taken from the Rig Veda?
Different websites say different amounts of verses are exclusive, but they all say less than 100.
One verse of the Sama Veda Samhita that is not present in the Rig Veda is verse 527, which is near the Aranya Archikah, Aranya Kandam section as you can see here:
ahamasmi prathamajā ṛtasya pūrvaṃ devebhyo amṛtasya nāma |
yo mā dadāti sa idevamāvadahamannamannamadantamadmi ||
I have been created before the creation of devtas and nobody can survive without consuming me. Those who donate me in Yagna etc., I protect them and bestow them with the result of pious deeds [punya].
This Richa is the basis of the Purushagati Saman, which is chanted by Jivas after attaining Moksha as I discuss in my question and answer here. And although it's not found in the Rig Veda, it is found in the Taittiriya Brahmana of the Yajur Veda; see my question here.
As I find more such Sama Veda-exclusive verses I may expand my answer.
EDIT: This PDF says "There are only the 1875 Saama Veda [mantras] that are unique to it; rest of them are mostly from Rg Veda with minor verbal differences and to music."
There are no such mantras which are in Sama Veda but not in the Rig Veda. That is, the text of all the Sama Veda mantras are already present in the Rig Veda.
The whole Vedas consist only of three types of mantras viz: the Riks, the Yajus & the Samans.
A Rik mantra has a metrical structure which is determined by the number of syllables in it. The number of syllables determine the metre (chandah) part of the mantra. Few examples of metres are Gayatri (composed of 24 syllables), Ushnik (28 syllables), Anushtup (32 syllables) etc.
A typical example of a Rik is the most famous Veda mantra called the Gayatri mantra of Viswamitra.
A Yajus will be in a short rhythmic prose. A typical example of such a mantra is the most famous mantra of Lord Shiva viz "namah shivaya" ( TS 220.127.116.11 ).
The text of a Saman mantra will be a Rik mantra, only difference being is in the method of chanting it. A Saman is chanted in a more elaborate way, more like singing.
For example, the number of mantras in Rig Veda ( Shakalya Shakha ) is 10,552.
And, the number of mantras in Sama Veda is 1875.
And, the text of all these 1875 mantras are already found in the Rig Veda samhita.
Some additional info regarding the distribution of Riks, Yajus and Samans among the four Vedas:
1- All the mantras that are present in Rig Vedas are Riks.
2- Atharva Veda has mostly Riks, but it also has a small number of Yajus mantras. The total number of mantras in Atharva Veda is 5038.
3- All the Riks are not present in the Rig Veda itself. That is, there are Rik mantras that are found in other Vedas but not in Rig Veda.
For example, TS of Yajur Veda has in all 4773 mantras. Of which, 3248 are Yajus and the remaining 1525 are Riks. And, among these 1525 Riks, 862 are found in the Rig Veda samhita. The remaining 663 Riks are not to be found in the Rig Veda.
So, not all Riks are found in the Rig Veda.
A rough Venn diagram indicating the overlapping among Vedas is as given below :
Abbreviations used :
TS 18.104.22.168- TS, Kanda 4, Prapathaka 5, Anuvaka 8, Mantra 11.