As-salaamu `alaykum warahmatullaahi wabarakaatuh.
Firstly, I have removed much from the above most, due to unfound claims, lack of evidence and plain simple errors which contradict the beloved Sunnah of our Messenger, sal-Allaahu `alayhi wasallam. I know that it was taken from the infamous Encyclopaedia whose authors are any one off the street, but I seriously caution people to study from that site, seeing as ANYONE can write whatever crap they want on there.
The Messenger of Allaah, sal-Allaahu `alayhi wasallam said,
"Whoever introduces into this matter of ours (religion) that which is not from it, will have it rejected."
This is the wording of the hadeeth in Saheeh Al-Bukhaaree. Muslim reports that the Messenger of Allaah, sal-Allaahu `alayhi wasallam said word to the effect of,
"Whoever does a deed that is not in accordance with this matter of ours, will have it rejected".
As the above wiki-definitions point our, the Tasbeeh refers to the usage of some stringed beads for dhikr. However, more correctly Tasbeeh simply means Glorifying Allaah, i.e. saying
Subhaan Allaah. It is just as Tasmee means saying the
Basmallaah. Just as Takbeer means to declare Allaah's greatness by saying
Allaahu Akbar. Just as Tahleel means saying
Laa ilaha ila Allaah, and just as Tasleem means saying
As-salaamu `alaykum and so-on and so-forth. However, many people primarily use the term Tasbeeh to refer to the object of beads, date stones and pebbles for dhikr, which is therefore what needs to be discussed. Imaam Ad-Daarimee recorded the hadeeth of Aboo Moosaa Al-Ash`aree, may Allaah be pleased with him, that he said to `Abdullaah Ibn Mas`ood, may Allaah be pleased with him, when he was the governor of Basrah,
"O Aboo `Abdur-Rahmaan! I saw something in the Masjid which I did not recognise. However, I think that what I saw is good, all thanks to Allaah." `Adullaah Ibn Mas`ood inquired as to what the matter was and Aboo Moosaa Al-Ash`aree answered by saying, "In the Masjid, I saw some men, with their heads shaven (a characteristic that the Messenger, sal-Allaahu `alayhi wasallam affiliated with the Khawaarij, see Saheeh Al-Bukhaaree 7007), sitting in groups, awaiting the prayer to start. Each group of men held stones in their hands and a man, the leader of the group would say to them, 'Say takbeer a hundred times', and they would recite takbeer a hundred times... The man would then order them to say Tahleel a hundred times, and they would recite it a hundred times. He would then order them to say Tasbeeh a hundred times, and they would recite it a hundred times." `Abdullaah Ibn Mas`ood asked if Aboo Moosaa if he said anything to those men, and Aboo Moosaa answered in the negative saying, "I waited for your opinion and your command."
Ibn Mas`ood said, "Why did you not order them to count their sins, and assured them that none of their good deeds will ever be lost."
`Abdullaah, Aboo Moosaa and others, went to the Masjid then to one of the groups and `Abdullaah asked them, "What is that which I see you doing?"
They said, "O Aboo `Abdur-Rahmaan! These are stones with which we count Takbeer, Tahleel and Tasbeeh."
`Abdullaah said, "Then count your evil deeds, and I assure you, none of your good deeds will ever be lost. Woe to you, Ummah of Muhammad, how fast you march towards your destruction (since innovations in the religion are a means of destruction)! These are the companions of your Prophet, sallAllaahu `alayhi wasallam, still plenty around (meaning that the people should take knowledge from them, refer to them, for they were the students of the Messenger, sal-Allaahu `alayhi wasallam). These are his clothes, they have not been worn off yet, and his pots and plates have not broken yet. By He in Whose Hand is my soul! You either follow a better guidance than that of Muhammad, sal-Allaahu `alayhi wasallam. Or else, you are opening a door to Dalaalah (misguidance; the Messenger, sallAllaahu `alayhi wasallam said that every bid`ah or innovation is a dalaalah. See Saheeh Muslim)."
They said, "O, Aboo `Abdur-Rahmaan, by Allaah! We only wanted to do that which is good."
He said, "How many a person who seeks to do righteously good, but does not achieve that (since they innovate into the deen, acts that will gain them no reward). The Messenger of Allaah, sallAllaahu `alayhi wasallam, told us that some people will come, who would recite the Qur'aan, but it will not reach beyond their throats (another characteristic of the Khawaarij that has been agreed upon. This means that they would not understand/act upon the Qur'aan)." `Abdullaah then parted with them.
The narrator of this hadeeth, `Amr Ibn Salamah mentioned that these same people fought along with the khawaarij against the companions in the battle of Nahrawaan. The hadeeth has been declared Saheeh by Shaykh Al-Albaanee. It is also worth mentioning that Ibn Taymiyyah said that the Muslim scholars consider the sects that follow their vain desires and by this, defy the Prophetic Law and the consensus of Muslims, as being amongst the khawaarij.
The above was taken from an excellent but lengthly discourse by our brother, Jalal Abualrub, may Allaah reward him for his efforts, entitled "Muhammad Ibn Abdul Wahhab His Lifestory and Mission".
There is also another Saheeh hadeeth, according to Shaykh Al-Albaanee wherein `Abdullaah Ibn Mas`ood saw many people using different types of objects for tasbeeh, and he adamantly opposed and prevented all of them (from such acts). The hadeeth has been mentioned by Al-Qurtubee, which I'll cite later inshaa' Allaah. Why was this noble companion so harsh against this practice? Because innovation in the religion is a means of destruction, and at the same time, the authentic Sunnah of the Prophet, sallAllaahu `alayhi wasallam tells us that we should use our hands for dhikr of Allaah,
"...and count using the joints of your fingers, because they will be asked and they will testify"
[Saheeh Sunan At-Tirmidhee (2835)]
For further reading, please read this article or clarification,
Did Imaam As-Suyootee Support Using Dhikr Beads.