And the Lord your God shall deliver them up to you (the children of Israel), you shall crush them, and utterly destroy them. You shall make no covenant with them nor show mercy to them. Nor shall you make marriages with them. You shall not give your daughter to his son, nor shall you take his daughter to your son . . .
But you shall deal with them in this way: you shall destroy their altars and smash in pieces their standing pillars, and cut to shards their groves and burn their graven images with fire (Deuteronomy 7:2 - 3, 5, HBFV).
The Hittites were a people who came from a region known as Asia Minor. They were a major power and an empire at the time when Joshua led Israel into the land (1405 B.C.). They first appear in the Bible as those who sold Abraham some land in which he could bury his beloved wife Sarah (Genesis 23:3 - 4, 10 - 11, 19 - 20).
The Canaanites are descendants of Canaan who was the son of Ham (one of Noah's three sons). They settled in the Land of Promise shortly after the flood.
The Girgashites (called Girgasites in the KJV Bible, Genesis 10:16) were Canaanites. Not much is historically known about these people. They may have inhabited the area east of the Sea of Galilee (Smith's Bible Dictionary) or possibly in the central part of Western Palestine (Illustrated Bible Dictionary).
The Amorites descended from Canaan (Genesis 10:15 - 16). They were known for producing giant people (Deuteronomy 3:11, Amos 2:9). King Sihon and the Amorites, at the time of Moses, lived just east of the Dead Sea and south of the river Jabbok. The Amorites, sometime before Israel entered Canaan, conquered the area previously populated by the Ammonites (Numbers 21:26).
Israel, under Moses, destroyed the Amorites and took all of their cities which included Heshbon (Numbers 21:21 - 26). After their conquest nothing more of note is mentioned about the Amorites in Scripture.
Perizzites, Hivites, Jebusites
The Perizzites were people who were scattered throughout the land. The Hivites were a people who ruled mostly around the area of Shechem. The Jebusites, who were descended from Ham, lived in and around the city of Jebus. After David became King, he and all the Israel fought the Jebusites, conquered them, and renamed Jebus to Jerusalem.
Israel did battle, though not specifically mentioned as a nation to conquer in Deuteronomy 7:1 - 2, the people of Bashan. The land of Bashan, at the time of Moses and Joshua, was ruled by King Og. The king was the last of the Rephaim or giants that lived east of the Jordan. He was so big that, conservatively, his bed was 13 1/2 feet long (4.1 meters) and 6 feet (1.8 meters) wide (Deuteronomy 3:11)!
Israel battled Og and his people at Edrei after they conquered the Amorites. The king, his sons, and all his people, are completely destroyed and their land is distributed among some of the Israelite tribes (Numbers 21:32 - 35, Deuteronomy 3:10, 12, Joshua 13:11 - 12).