In the Hebrew tradition, any time the children of a person is being listed it follows in the order of their birth. In other words the name of the eldest child is always written first and the rest follow in the order of their birth.
So the list of the children of Jacob goes like this; Reuben, Simeon, Levy, Judah and so on (Gen. 35: 22-26). The list of David's children also goes like this: Amnon, Daniel, Absalom, Adonijah, Shephatiah (1Chr. 3:1-3).
In that same vein the list of the children of Noah goes like this: Shem, Ham and Japheth (Gen. 9:18 and Gen. 10: 1). This clearly suggests that Japheth was the youngest son of Noah and not Ham.
In spite of this strong indication that Ham was not the youngest son of Noah, many a Bible commentator have laid the Noah's curse on Ham. Some even go to the extent of justifying the slavery of Africans as biblical since two of the children of Ham; Egypt and Libya built their kingdoms in Africa.
But was the curse really laid on Ham? Let's read the curse verbatim in Gen. 9:24-27; "24 When Noah was sober again and learnt what his youngest son had done to him, 25 he said 'a curse on Canaan. He will be a slave to his brothers. 26 Give praise to the LORD, the God of Shem. Canaan will be the slave of Shem. 27 May God cause Japheth to increase. May his descendants live with the people of Shem. Canaan will be the slave of Japheth."
If you read the curse carefully you would realize that it was laid solely on Canaan who was a grandson of Noah and a son of Ham. The other sons of Ham were not mentioned in the curse at all, hence were not affected.
If the curse was meant for Ham, the names of his other children would have, of course, been mentioned.
The problem is that in the Hebrew language, similar expressions are used for youngest son and grandson. So the bible translators, instead of translating the grandson correctly as the one who was cursed, mistakenly translated it as the youngest son.
But even if we assume, without admitting, that it was the youngest son who was cursed, the youngest son of Noah was not Ham but Japheth.
Ham was neither the youngest son nor a grandson of Noah, hence it was not Ham who was cursed by Noah but Canaan.