The short list of textual variants below is nearly obsolete now, since recently much more extensive and thorough documentation has been published elsewhere, e.g. Samuel Green's article The Seven Readings of the Qur'an and in chapter six of Brother Mark's monumental work A `Perfect' Qur'an. However, we will keep this article in place for documentation sake because of the discussion that it created.
Apart from other earlier variant text, there are two different texts of the Qur'an currently in print, named after their respective 2nd-century transmitters Hafs (from Kufa) and Warsh (from Medina).
The Hafs text is the more common and used in most areas of the Islamic world. Warsh is used mainly in West and North-West Africa as well as by the Zaydiya in Yemen.
The textual differences listed here are mainly taken from the article "The Value of the Hafs and Warsh transmissions for the Textual History of the Qur'an" by Adrian Brockett, published in "Approaches to the History of the Interpretation of the Qur'an", edited by Andrew Rippin, Clarendon Press, Oxford, 1988.
These readings of Hafs are from the `usual' Qur'an text [used in Yusuf Ali for example] while the Warsh text is found in the Qur'an published by the Tunis Publishing Company in 1996.
Sura Hafs Warsh 2:132 wawassa wa'awsa (Al-Dani mentions that Abu `Ubayd saw wa'awsa in the imam, the mushaf `Uthman) 3:133 wasari'u sari'u 5:54 yartadda yartadid (Al-Dani quotes that Abu `Ubayd saw yartadid in the imam) 3:81 ataytukum ataynakum 2:259 nunshizuha nunshiruha 2:140 taquluna yaquluna 2:125 wattakhidhu wattakhadhu 2:9b yakhda'una yukhadi`una 2:214 yaqula yaqulu 3:37 wakaffalaha wakafalaha 20:63 In hazayni Inna hazani
There are many more variants, but the above should be enough to show that there are indeed textual differences in currently printed and recited Qur'ans.
Muslims can claim that the variants are small and the difference in meaning insignificant for the general message of the Qur'an, but they cannot honestly claim that there are no variants.
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