Those who believe (in the Qur'an), and those who follow the Jewish (scriptures), and the Christians and the Sabians,- any who believe in Allah and the Last Day, and work righteousness, shall have their reward with their Lord; on them shall be no fear, nor shall they grieve. -- 2:62Other verses of the Qur'an deny this:
If anyone desires a religion other than Islam (submission to Allah), never will it be accepted of him; and in the Hereafter He will be in the ranks of those who have lost. -- 3:85
This apparent contradiction is resolved by some principal proponents of the Shafi'i madhhab as follows:
Suddi states that (2:62) was revealed about the former companions of Salman the Persian when he mentioned them to the Prophet, relating how they had been, saying, "They used to pray, fast, and believe in you, and testify that you would be sent as a prophet." When he had finished praising them, the Prophet replied, "Salman, they are the denizens of hell," which came to discomfit Salman greatly, and so Allah revealed (2:62).In other words, salvation for non-Muslims was possible "until the coming of Muhammad." After that point, "those of them who did not follow Muhammad... were lost (to Hell)."
The faith of the Jews was that of whoever adhered to the Torah and the sunna of Moses until the coming of Jesus. When Jesus came, whoever held fast to the Torah and the sunna of Moses without giving them up and following Jesus was lost.
The faith of the Christians was that whoever adhered to the Gospel and precepts of Jesus, their faith was valid and acceptable until the coming of Muhammad. Those of them who did not then follow Muhammad and give up the sunna of Jesus and the Gospel were lost.
The foregoing is not contradicted by the hadith relating that (2:62) was followed by Allah revealing (3:85), for the hadith merely confirms that no one's way or spiritual works are acceptable unless they conform to the Sacred Law of Muhammad, now that he has been sent with it. As for people prior to this, anyone who followed the messenger of his own time was guided, on the right path, and was saved. (Reliance of the Traveller, 848-849)
Some polemicists will play semantic games with the words "Islam", defining it as "submission to God" in order to make it appear that 3:85 allows for a Jew or a Christian to be saved. Indeed, even the above translation by Yusuf Ali seems to be doing that. However, traditional commentaries are much more forthright and they exegete the Qur'an more honestly: Islam teaches that non-Muslims cannot be saved.
Of course, I have only provided the Shafi'i interpretation; I believe it will be representative of the other major schools, but if I find otherwise, I will make a note.
As a final note, I would like to add that the Shafi'i interpretation is the best case scenario for the Muslims. They've got a dilemma: either the Shafi'i interpretation is accurate, or these two verses pose a contradiction. If the Shafi'i interpretation is accurate, it doesn't make good sense of the present tense used in 2:62. If there's a contradiction, well, it's clear what the implications would be. I actually think the latter is a better conclusion, but so as to offer the benefit of the doubt to Muslim exegetes and commentators (and the virtually unanimous decisions of the fuqaha), I will concede the Shafi'i interpretation.