Learn German: Der Junge hat keinen Rucksack. - The boy does not have a backpack.

Rucksack is a masculine noun (der Rucksack). Because it is the direct object being 'had' in this sentence, it needs to be in the accusative case. For masculine nouns in the accusative case, the negative article kein adds an -en ending to become keinen.

Could I say Der Junge hat nicht einen Rucksack to mean 'The boy does not have a backpack'?

You will almost never hear a German speaker say that. In German, when you want to negate a noun that would normally use an indefinite article like 'a' or 'an' (like einen Rucksack), you use a form of kein instead of nicht. So 'does not have a backpack' naturally becomes hat keinen Rucksack.

The word Junge ends in '-e'. Doesn't that usually mean a noun is feminine?

Often, yes! Many nouns ending in '-e' are feminine. However, Junge means 'boy', and because it refers specifically to a male person, it is a masculine noun. That is why it uses the masculine article der.

Why doesn't der Junge change to the accusative case too?

Der Junge is the subject of the sentence—he is the one doing the having. The subject is always in the nominative case, which is the basic dictionary form. Only the direct object (the thing being had, which is the backpack) changes to the accusative case.