We don't get to pick our parents. If you are in a family with an abusive, weak or troubled mother, there are steps you can do to protect yourself and hopefully your siblings. Remember that you alone are responsible for creating a happy and fulfilling life for yourself.

[edit] Steps

Create a good sounding board for yourself to give your life some needed perspective. It is important that you do this as writing and not by talking to someone. That comes later in the process. Start a journal or a blog but make sure it is not going to be read by your mother. The objective is to heal yourself, become stronger and remove toxic behavior from your life, not hurt your mother.
Think very hard and make detailed lists regarding your mother. Why is she so unhappy? What were her parents/family life like? What are her frustrations or failed dreams for herself? How can you avoid falling into a pattern to not become like her? What are her expectations for herself and you? Your siblings? What are your expectations from her and your own behavior?
Start to distance yourself-this is the hardest part but you absolutely need to do this step. Imagine you are from another planet and you are observing her dialogue and patterns of destructive behavior. What are her triggers? How do you respond to her outbursts or her drama? Write this all down in your journal. Start with your behavior towards her. Write down pieces of any emotional conversation and look at it. Are you feeding her behavior in any way or adding fuel to the fire. If you are then stop immediately.
Discover how unpleasant dialogue/fights with her starts and when. Note the hot spots. Is it every time you talk or just around certain people? What are the triggers? Self knowledge is power. Your brother and sisters may need help but you need to help yourself first to help them.
Understand that for your mother to strike out at you or favor one sibling over another has to do with her short comings as a person. She might be aware or oblivious to how she is being so damaging. Emotional behavior is the hardest to change but you can become less involved and more objective. It will make you stronger.
Protect yourself. For six months be only the observer not caught up in the drama. She will notice a change in you and may increase her attacks. Stay calm, observe and keep writing.
Talk to and interview each sibling. Tell them you are trying to build a happier family life and need their help.
Ask them their observations about your mother and what are the triggers for them around her. You will start to see the big picture of your family and its troubles but this could take a year or more. Keep writing it out.
Reflect on whether it is healthy to keep a relationship with her. Some people are so toxic and damaging to be around that they will try to destroy you. If this is the case-leave the relationship and not talk/visit her for an allotted amount of time. Write her a letter and tell her you need some space but will contact her when the time is right. The time might never be right but you saved yourself.
Believe that being a child of a unhappy person is very hard and give yourself the room to be happy and create a life. Start one step at a time becoming more independent. In the long run, what your mother thinks of you is NOT who you are. Her distorted opinion of you or your siblings don't count much if you can understand how hurtful and destructive it is. Your job is not to make her happy. That does not make you a "bad, selfish, etc" person but a healthy one.
Help your siblings when you are freed from her grasp. Find solutions that work for you in dealing with her and tell them your methods. Tell them you want them to have positive self images of themselves and to be strong. Role model healthy mental behavior towards them and her. Console them if they are in pain.
Avoid the trap of guilt. It is the number one reason people stay in destructive relationships. You are responsible for yourself not her.

[edit] Tips

Set a timer or record your phone call conversations. It may help you end conversations or gain some needed perspectives.
Don't tell everyone in the family what you are doing-it might get back to your mom and create a new drama you don't need.
Don't involve your father until you understand that he has problems of his own. He is married to this person and it will get back to her. Remember the object is to heal not be destructive and hurtful like her.
Do tell a best friend or a mate. First make sure they can be supportive and understanding of your situation.
Most people have horror mother stories either their own or a friends. How you handle your own behavior is what matters.
Give yourself time to grieve over what you needed but did not get. Or the fact that you did not want this kind of person in your life. But don't wallow in it for years, self pity is destructive.

[edit] Warnings

Protect your kids/husband if needed. Don't let them get caught up in the drama. Again role model "strength" in dealing with a destructive person for your kids. It will serve them well in life.
Never resort to being nasty with her. Set your boundaries with her. Screaming or cursing will just make you feel bad about yourself. You can just tell her politely "I am hanging up now" or :I am leaving". Then do it! You have the right to end any conversations with people who put you down or humiliate you. You also have the right to be angry at someone you love.
Sometimes we have to completely leave the relationship. It is just too damaging and everyone is ALLOWED to make that personal decision with any guilt.