Does Exodus 20:4-6 and other passages teach generational curses?

No. In Exodus 20:4-6 the subject is idolatry. Regarding those who commit idolatry, we learn that God would visit the iniquity of the fathers upon the children to the third and fourth generations of those who hate Him. Notice, the text says "generations of those who hate Me." Therefore, we see that God would punish those who imitate their fathers' idolatrous actions. In other words, there are sinful patterns that children see in their parents that they often times replicate in their own lives. It is not that God has placed a curse on the people. It is not as if the children are obedient to God but God still punishes them because of their parents' disobedience. The point is that they are idol worshipers just like their parents were. In fact, verse 6 shows that God shows mercy to those who love Him, irregardless of their parents' disposition towards God. The contrast that we have in verses 4 and 5 is between those who hate God and those who love Him. The reason for it affecting the third and fourth generations is that the effects of idol worship is that it leads to children becoming accustomed to it, and they often times replicate it in their own lives.

Other passages to consider are listed below:

• Deuteronomy 24:16: Moses states that fathers would not be put to death for their children's sins and children would not be put to death for the fathers' sins. Notice that he says, "A person shall be put to death for his own sin."
• Ezekiel 18: This passage in fact the entire chapter - shows that God never agreed with the false saying of the people: "The fathers have eaten sour grapes, and the children's teeth are set on edge." In other words, rather than taking responsibility for their own actions, they attributed their sinful ways to their parents. However, notice that God said that they were to no longer use that proverb in Israel. He went on to say that the soul who sins shall die and that the one who is lawful and right shall live (Ezekiel 18:4-9).
• Jeremiah 31:27-30: We see the same thing here. Every one dies for his own iniquity. If one "eats the sour grapes, his teeth shall be set on edge."