My 9 month old cries a lot when things are taken away from her - like her toys or anything she is interested in. Is this normal. Any ideas on how I can get her to stop throwing "tantrums"

In such case, you need to reinforce the behaviour you want. If she cries do not give her the item again. However, please gauge if there is any other underlying reason to the tantrum such as lack of sleep, hunger, etc.. Try to divert her attention once the toy has been taken away. 9mths is still really young.