Muslim scholars teach that Muslims should generally be truthful to each other, unless the purpose of lying is to "smooth over differences."
There are two forms of lying to non-believers that are permitted under certain circumstances, taqiyya and kitman. These circumstances are typically those that advance the cause Islam - in some cases by gaining the trust of non-believers in order to draw out their vulnerability and defeat them.
Qur'an (16:106) - Establishes that there are circumstances that can "compel" a Muslim to tell a lie.
Qur'an (3:28) - This verse tells Muslims not to take those outside the faith as friends, unless it is to "guard themselves."
Qur'an (9:3) - "...Allah and His Messenger are free from liability to the idolaters..." The dissolution of oaths with the pagans who remained at Mecca following its capture. They did nothing wrong, but were evicted anyway.
Qur'an (40:28) - A man is introduced as a believer, but one who must "hide his faith" among those who are not believers.
Qur'an (2:225) - "Allah will not call you to account for thoughtlessness in your oaths, but for the intention in your hearts"
Qur'an (66:2) - "Allah has already ordained for you, (O men), the dissolution of your oaths"
Qur'an (3:54) - "And they (the disbelievers) schemed, and Allah schemed (against them): and Allah is the best of schemers." The Arabic word used here for scheme (or plot) is makara, which literally means deceit. If Allah is deceitful toward unbelievers, then there is little basis for denying that Muslims are allowed to do the same. (See also 8:30 and 10:21)
Taken collectively these verses are interpreted to mean that there are circumstances when a Muslim may be "compelled" to deceive others for a greater purpose.
From the Hadith:
Bukhari (52:269) - "The Prophet said, 'War is deceit.'" The context of this is thought to be the murder of Usayr ibn Zarim and his thirty unarmed men by Muhammad's men after he "guaranteed" them safe passage (see Additional Notes below).
Bukhari (49:857) - "He who makes peace between the people by inventing good information or saying good things, is not a liar." Lying is permitted when the end justifies the means.
Bukhari (84:64-65) - Speaking from a position of power at the time, Ali confirms that lying is permissible in order to deceive an "enemy."
Bukhari (50:369) - Recounts the murder of a poet, Ka'b bin al-Ashraf, at Muhammad's insistence. The men who volunteered for the assassination used dishonesty to gain Ka'b's trust, pretending that they had turned against Muhammad. This drew the victim out of his fortress, whereupon he was brutally slaughtered despite putting up a ferocious struggle for his life.
Muslims are allowed to lie to unbelievers in order to defeat them. The two forms are:
Taqiyya - Saying something that isn't true.
Kitman - Lying by omission. An example would be when Muslim apologists quote only a fragment of verse 5:32 (that if anyone kills "it shall be as if he had killed all mankind") while neglecting to mention that the rest of the verse (and the next) mandate murder in undefined cases of "corruption" and "mischief."
TheReligionofPeace - Islam: Taqiyya and the Truth