Rather than relying on shoddy hate sites/Christian missionaries to educate us about taqiyyah we shall rely on SCHOLARLY authority – largely in the form of R. Strothmann’s relevant section in “Shorter Encyclopaedia of Islam” (by H.A.R. Gibb and J.H. Kramers) and Cyril Glasse’s Concise Encyclopedia of Islam
What is “Taqiyyah”, “Takiya”, “Taqiyya”?
This term is spelt variously; “taqiyyah”, “takiya” or “taqiyya”.
“Takiya (A.), caution, fear (see glossarium to Tabari S.V. T-K-A) pr kitman, “disguise” is the technical term for dispensation from the requirements of religion under compulsion or threat of injury.” 
“Taqiyyah (From the root word waqa “to safeguard”; “self-protection” and hence “dissimulation [in order to protect oneself]”).” 
So, taqiyyah (takiya, taqiyya) is concerning dissimulation due to force – i.e. when an individual is forced to conceal.
Sadly, Islamophobes and Christian missionaries – in order to obtain an unchecked platform and/or demonise Muslims – have misapplied this term in their exaggerated claims of “Muslims are allowed to lie to the unbelievers”.
At what level of force is Takiya (Taqiyyah, Taqiya) justified?
“But an individual is not justified in takiya nor bound to hidjra [emigration] if the compulsion remains within the endurable limits, as in the case of temporary imprisonment or flogging which does not result in death” 
So, this make a mockery of the Islamophobes’ general suggestions of “Muslims are allowed to lie to the unbelievers” as even under threat of imprisonment and flogging Muslims are not justified in takiya. The level of force which justifies oneself in takiya is that of an unbearable level.
Takiya (taqiyya, taqiyyah) and the type of lies…
One may ask, what type of “disguise” is allowed under takiya (taqiyyah, taqiyya)?
Let’s be clear about takiya (taqiyyah, taqiyya); “The principle of dissimulation of one’s religious beliefs in order to avoid persecution or imminent harm, where no useful purpose would be served by publicly affirming them.” 
So takiya (taqiyyah, taqiyya) is not used to convert folk to Islam nor is it used in Islamic text books or anything of such a nature. It is simply a form of concealment used to avoid persecution!
For further clarity, we are not talking about general, everyday fibs here, thus the ethical question of dishonesty is bypassed:
“The ethical question whether such forced lies are nevertheless lies, such a forced denial of the faith nevertheless a denial, is not put at all by one “who conceal himself” as he is not in a state of confidence which would be broken by lies or denial.” 
Sadly, our Islamophobic counterparts attempt to convince the gullible that takiya (taqiyyah, taqiyya) allows Muslims to lie (or conceal) about aspects of their faith (Islam) as well as lie in general.
Recently, Islamophobes were accusing Senator Keith Ellison of taqiyyah. Try learning what taqiyyah (takiya, taqiyya) is before accusing folk of it, you may just look less silly if you take this advice on board!!!
Famous case of Taqiyyah (Taqiyya, Takiya)
A common example of takiya (taqiyyah, taqiya) involves a Muslim (Ammar B. Yasir, a companion of the Prophet Muhammad, p) being forced to worship idols and insult the Prophet of Islam.  
The level of force the polytheists applied on Ammar bin Yasir can be imagined by Amr bin Maymoon’s statement, “The polytheists tortured Ammar with fire”. 
“Abu Ubaydah bin Muhammad bin Ammar bin Yasir said: The polytheists seized Ammar and they did not let him off until he was forced to insult the Messenger of Allah and say good things about their deities” 
Ammar bin Yasir told Prophet Muhammad (p) of what he was forced to say.
“The Prophet (p) said: “Say it again if they ask (i.e. force) you to do so”.” 
So, in order to avoid such torture the Prophet allowed Ammar bin Yasir to use “taqiyya”
If Jesus (p) had done the same, our Christian friends would have lauded it as an act of piety and mercy. Instead we see Islamophobes exaggerating this form of concealment in order to demonise Muslims. It’s a crazy old world!
Taqiyyah and the Shi’ites (Shia)
"It is, however, associated most closely with the Shi’ites who practiced taqiyyah systematically and widely during periods of Sunni domination to hide their beliefs from Sunni Muslims. "
Obviously, if these Shi’ites felt they would have been persecuted for publicly announcing their shia beliefs, one can understand why they concealed (used taqiyya) their beliefs.
Is taqiyyah allowed in the Quran?
Our Islamophobic friends jump up and down in joy whilst proclaiming taqiyyah (taqiyya, takiya) is allowed in the Quran. Let’s analyse (via scholarship) the two Verses they cite.
Quran 16:106 and taqiyyah (taqiyya, takiya)?
Whoso disbelieveth in Allah after his belief - save him who is forced thereto and whose heart is still content with the Faith - but whoso findeth ease in disbelief: On them is wrath from Allah. Theirs will be an awful doom. [Pikthal translation of the Quran 16:106]
The reason for this verse is unanimously said to have been the case of Ammar b. Yasir, whose conscience was set at rest by this revelation when he was worried about his forced worshipping of idols and objurgation of the Prophet. 
The story of Ammar bin Yassir is relayed earlier in the article (see above).
Tabari says on Sura 16:106 (Tafsir, Bulak 1323 sqq.24.122): If any one is compelled and professes unbelief with his tongue, while his heart contradicts him, to escape his enemies, no blame falls him on him, because God takes his servants as their hearts believe” 
The Quran’s (16:106) allowance of uttering disbelief whilst under extreme force is hardly justification for the outrageous smears the Islamophobes propagate.
Quran 3:28 and taqiyyah (taqiyya, takiya)?
Let not the believers take disbelievers for their friends in preference to believers. Whoso doeth that hath no connection with Allah unless (it be) that ye but guard yourselves against them, taking (as it were) security. Allah biddeth you beware (only) of Himself. Unto Allah is the journeying. [Pikthal translation of the Quran 3:28]
This Verse instructs Muslims to not take the unbelievers as patrons over the believers but does allow for this in the case of fear. Tuqatan is used here (a verbal noun of taqiyyah). Tafsir Jalalayn explains:
“unless you protect yourselves against them, as a safeguard (tuqātan, ‘as a safeguard’, is the verbal noun from taqiyyatan), that is to say, [unless] you fear something, in which case you may show patronage to them through words, but not in your hearts” [Tafsir Jalalayn – 3:28]
It is hardly something Islamophobes can latch onto as evidence for their demonization of Muslims as this Verse allows concealment (taqiyyah, taqiyya, takiya) in the case of fear (i.e. to avoid persecution). We are essentially back to where we started as initially stated on taqiyyah:
Takiya (A.), caution, fear (see glossarium to Tabari S.V. T-K-A) pr kitman, “disguise” is the technical term for dispensation from the requirements of religion under compulsion or threat of injury. 
Taqiyyah (From the root word waqa “to safeguard”; “self-protection” and hence “dissimulation [in order to protect oneself]”). 
Taqiyya is acceptable till the Day of Judgement
Ibn Kathir, a prominent authority writes, "Whoever at any time or place fears their [infidels'] evil may protect himself through outward show." As proof of this, he quotes Muhammad's companion, al-Hassan, who said, "taqiyya is acceptable till the Day of Judgment [i.e., in perpetuity]." http://en.wikipedia.org/wiki/Taqiyya
Islamophobes make a big deal out of Muslims believing taqiyya (taqiyyah, takiya) is acceptable to this very day and beyond. So what? There is NO issue here whatsoever.
Think about it, if, in the future, an extreme Christian/Hindu/Islamophobe put a gun to a Muslim’s head and asked him to denounce Islam in order to preserve his life would you really have qualms in the fact the Muslim would be allowed (according to Islam) to do so in order to protect his life?
Abraham (p) and taqiyyah
In the Biblical account of Abraham, Sarah and Pharaoh we notice Abraham (and Sarah) concealed the fact Sarah was his wife as he feared death:
When the Egyptians see you, they will say, 'This is his wife.' Then they will kill me but will let you live.
Say you are my sister, so that I will be treated well for your sake and my life will be spared because of you.” [Genesis 12:12-13 NIV]
Where are the Christian Islamophobes to demonise Abraham, Sarah and the Bible? Nowhere!
Why are people not exaggerating this to mean the Bible allows Jews and Christians to lie to non-believers just as they do against Muslims in the case of taqiyyah? The answer is hypocrisy as Islamophobes work an anti-Muslim agenda assiduously whilst refraining from using the same absurd modes of exaggeration/deception against Christians and Jews!
The “Apostle” Paul and taqiyyah?
Paul, in Corinthians 19, was using a strange tactic to convert people. So strictly speaking, Paul did not practice taqiyya as he was not under threat of harm and his “concealment” was in the avenue of evangelism rather than that of self-protection. Paul was concealing himself as a Jew (to convert Jews), as a gentile (to convert gentiles) and as the weak (to convert the weak).
19 Though I am free and belong to no one, I have made myself a slave to everyone, to win as many as possible.
20 To the Jews I became like a Jew, to win the Jews. To those under the law I became like one under the law (though I myself am not under the law), so as to win those under the law.
21 To those not having the law I became like one not having the law (though I am not free from God’s law but am under Christ’s law), so as to win those not having the law.
22 To the weak I became weak, to win the weak. I have become all things to all people so that by all possible means I might save some. [Corinthians 9:19-22, NIV]
Of course, Christian apologists would extend explanation towards Paul’s strange actions in order to exonerate him of the allegation of deception but you can see why there is a potential cause for concern here – especially in the light of the numerous deceptive episodes involving Christian missionaries ever since Paul’s strange actions.
Why are our Christian Islamophobes not concluding Paul’s actions to mean all Christians can lie whilst evangelising folk?
I have caught Christian missionaries, on numerous occasions, lying to convert folk to Christianity. If you want to exegete this New Testament account to mean Christians are allowed to use deception whilst evangelising you will have a stronger case than that of the Islamophobes’ exaggerations on Muslim allowance of taqiyyah (concealment due to fear).
Lying about the Prophet Muhammad (p)
Islamophobes, in an attempt to obtain an unchecked platform, do suggest Muslims misinform (“use taqiyya”) about the Prophet Muhammad (p). This is an utter absurdity as it is a grave sin for a Muslim to misinform about the Prophet Muhammad as the Prophet stated:
“Whoever lies about me intentionally shall take a place for himself in hell” (al-Adhkar (y102), 510-12) 
In fact, presenting misinformation about the Prophet (p) was considered an extreme offense amongst early Muslim communities:
Habib ibn ar-Rabi’ said that it is disbelief to alter his [Prophet Muhammad’s] description and its details. The one who does that openly is an unbeliever. He is asked to repent. 
So much for the Islamophobes claims of “Muslims using taqiyyah” regarding Prophet Muhammad (p).
Taqiyyah (taqiya, takiya) is not something to be writing home about. To use this practice to brandish Muslims as untrustworthy (or to demonise them) is unscholarly and unjust.
If you do encounter an anti-Muslim bigot on the internet crying “taqiyya” (there are plenty about), please do send him/her away educated.
There are a number of Islamophobes who do make cash and political inroads out of demonising Muslims with all this exaggeration concerning taqiyyah (takiya, taqiyya) amongst other absurd claims concerning Muslims. These folk do influence other folk on the internet to propagate these misconceptions – thus it is our job to present the truth to counter the many anti-Muslims deceptions out there.
"During times of universal deceit telling the truth becomes a revolutionary act" - George Orwell
 Article by R. Strothmann, Shorter Encyclopaedia of Islam, H.A.R. Gibb and J.H. Kramers, Fourth impression, 1995, E.J. Brill Leiden. New York. Koln p. 561 - 562
 The Concise Encyclopaedia of Islam, Revised Edition, Cyril Glasse, Stacey International, 2001, p450-451.
 Men and Women around the Messenger, Sa’d Yusuf Abu ‘Aziz, Translated by Suleman Fulani, Darussalam, 2009, p. 286-287
 Reliance of the Traveller, Translated by Nuh Hamim Keller – Amana Publications, 2008, r8.0, p 747
 Muhammad, Messenger of Allah – Ash Shifa of Qadi Iyad, translated by Aisha Abdarrahman Bewley, Madinah Press, 2004, p. 387