The Book of Genesis does not mention what type of tree it was at all. In the Hebrew, Greek, and Latin versions of the Bible, the fruit is only referred to as a fruit, never an apple. The idea that the Tree of Knowledge was an apple tree comes from the fact that the Latin word for apple ("malum") and the Latin word for evil ("malum") are almost identical. The only difference is that the "a" vowel is long in the word for apple but short in the word for evil. The idea of the fruit being an apple does come from Latin Christian commentaries in Late Antiquity and the Middle Ages.

In Greek Orthodoxy and Judaism, the fruit of knowledge is often interpreted as a pomegranate or, more rarely, a grape or fig. As far as I know, Greek Orthodoxy only considers the fruit to be a pomegranate. In Judaism, the seeds of a pomegranate symbolize the deeds you're supposed to do as an observant Jew, so in eating the fruit, Adam and Eve have taken on this burden. Rabbi Meir suggests that it was a grape (because grapes make wine.) Rabbi Nechemia suggested that the fruit was a fig using the following chain of reasoning:

Q: If Adam and Eve chose to cover their nakedness with fig leaves, why did they choose these and not some other leaves?
A: Because they were close at hand.
Q: Why were they close at hand?
A: Because that must be the tree from which they ate.

I know nothing of Muslim interpretations of the fruit.