Misconception: Must be "Muslim" or you will go to Hell

Background: Some think that a person must be a Muslim to enter paradise/heaven, and if not, they will go to Hell once they die.

The Quran repeatedly states the criteria for success as monotheism, recognition of accountability and being righteous:

Surely those who believe, and those who are Jews, and the Nazarenes*, and the Sabians, whoever believes in God and the Last day and does good, they shall have their reward from their Lord, and there is no fear upon them, nor shall they grieve. [2:62]

Those who believe, and those who are Jewish, and the Sabiens, and the Nazarenes*; whoever of them believes in God and the Last Day and does good works, then they will have nothing to fear nor will they grieve. [5:69]
*commonly translated as "Christians" but more likely refers to the followers of Jesus of Nazareth, hence Nazarenes.

The Quran also states that there are some of "the people of the book" (i.e. followers of previous revelations) that are righteous and will be rewarded:

And if the followers of the Book had believed and guarded (against evil) We would certainly have covered their sins and We would certainly have made them enter gardens of bliss.
And if they had observed the taurat* and the injeel* and that which was revealed to them from their Lord, they would have enjoyed happiness from above and beneath them, there is a party of them keeping to the moderate course, and (as for) most of them, evil is that which they do.
*commonly translated as Torah and Gospels respectively.

They are not all alike; of the followers of the Book there is an upright party; they recite God's communications in the night and they adore (Him).
They believe in God and the last day, and they enjoin what is right and forbid the wrong and they strive with one another in good deeds. These are of the righteous.
And whatever good they do, they shall not be denied it, and God knows those who are forethoughtful.

And from among the people of Moses are a community who guide with the truth and with it they do justice.

READ - click to look up verse references