It is easy to take a few verses and try to draw a conclusion about women being inferior, but there are so many verses that run counter to this common understanding.
We start near the beginning of the Bible:
The LORD God said, "It is not good for the man to be alone. I will
make a helper suitable for him." (NIV, Genesis 2:18)
The Hebrew word for helper, ezer, is also used to describe God himself in Psalms 33:20, 70:5, 115:9-11.
So, we have that women were made to be a helper, not a servant to men, and, don't remember where this came from but, God didn't pick a bone from his feet to be under man, nor from his head to be over him, but from his rib to be equal with him.
Then in Genesis 2:27-28 and Genesis 5:1-2 they were created in the likeness of God.
In Genesis 3:16-19, when they were both booted out of the Garden, both were punished by God.
In the OT we have writings and examples of influential women, such as: Deborah, Esther, Hannah, Huldah, Jochebed, Miriam, Noadiah, Rachel, Rebekah, Rahab, Ruth and Sarah
In the 10 Commandments we also see that we need to honor both of our parents: Exodus 20:12
In the NT Mary and Elizabeth were models of virtue and faithfulness as both put their trust in God: Luke 1:26-45.
Jesus allowed women to travel with him and the Apostles, Luke 8:1-3, though women were normally relegated to just staying at home.
"Proper" Jews didn't talk with Samaritans, and especially the women, but Jesus had a long talk with the woman at the well: John 4:4-30, 39-42.
Women were generally not well educated, nor given roles in religion, but a lady named Mary sat at the feet of Jesus while he taught, and he suggested her sister Martha do the same: Luke 10:38-42.
In the early church women were held as near-equals and given positions of authority: Acts 1:12-14, 9:36, 16:14, 18:24-26, 21:7-9, Romans 16:1-16.
We also have that there is no difference based on gender, status or wealth, for example, in the early Christian church: Galatians 3:26-29.
OK, so we see in 1 Corinthians 14:33-35 that women shouldn't speak in church, but in 1 Corinthians 11:5 we see that women were allowed to pray and prophecy, so if we look at 1 Cor 14 there was some problem in the church in Corinth, as this was about some disruptive practices, so it may be that some women were causing issues based on talking too loud or often, but 1 Cor 14:33-35 was not to be taken as a church norm.
We see in Ephesians 5:21-30 that though men should be in charge of the family, women are not slaves, but should be treated with honor by the husbands.
So, if we remember to love each other as we see in 1 Cor 13, and treat our wives with the same respect as Jesus showed to the church by willingly being crucified, then we should see that women are treated carefully, with love and respect.
To see how modern times change the role of women we can look at Mary Magdalene (http://www.marypages.com/MaryMagdalene.htm).
She was not a prostitute, but was a vital part of Jesus' ministry, as is evident as the first person He appeared to when He was resurrected was her, not Peter. It was in the middle ages I believe that the story that she was a prostitute was created.
She was called the Apostle to the Apostles,and was seen to have been held in high regard by the early Church.
This would have been unusual for a woman to be seen this way, but the early Church, and Jesus, were not always bound by cultural mores, but there were times when they did give in, such as telling women to wear veils, as they were focused on spiritual issues and not on worldly ones (2 Corinthians 5:17).