What does the bible say about women in leadership?

It will be impossible to answer this question, or even do it justice, in such a small space. However, at a 10,000 ft. view there appear to be three types of passages on women's roles in leadership.

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• Normative.  These are passages where the biblical author is describing the way things ought to be.  Generally these passages endorse women in leadership. (Acts 2:17-18, Galatians 3:28, 1 Corinthians 7:4-5, Philippians 4:2-3).
• Descriptive. These are passages that neither endorse nor prohibit women in leadership, but show women acting in the gifts or potentially fulfilling a leadership role. (Matthew 28:9-10, 1 Corinthians 11:4-5, Acts 21:8-9, Romans 16:1-4). 
• Problematic. These are passages that are providing correction to a church and prohibit women in leadership either generally, or in relation to cultural or situational problems that were occurring at the time of the writing.  (1 Timothy 2:8-15, 1 Corinthians 14:34-35, 1 Corinthians 11:11-12, 2 Timothy 4:19).

Four of the main interpretations of these passages include:

• Traditional Silence view. Women are forbidden to have authority over a man and should remain silent, thus excluding them from ministry.
• Complementarian view. Women may exercise their gifts for ministry, except when that would involve authority over men.  In these arenas  women should submit to men due to the created order.
• Plural Ministry view. Women my participate in ministry because biblically ordination does not mean to confer authority over another.  Since true ministry is service (not authority), authority in a church does not rest with an individual. 
• Egalitarian view. Women have full equal authority in both Creation and Redemption, thus no restrictions should be emplaced on women serving in ministry.

While an important topic, we must remember that the primary purposes of the church, and impart grace and charity to those who may disagree with the interpretation we feel is best. 

(Roy King - Women in Leadership: Passages and Views)