M.R.
The most effective way I got my daughter (recently turned 4 y.o) to stop was place her in her room while I explained that although no one wanted to hear scream and bang on the floor, she was more than welcome to come out when she stops throwing her fit. Once she comes out calm, cool, and collected I spend time with her in a positive way by including her in my activities (not discontinuing them). This has been effective in extinguishing undesirable behavior but may take several times of doing this.
At times when I do not have time to argue, such as getting ready in the mornings, I tell her that she will lose a privilege (watching cartoons) or access to an item that she loves (toys). The privilege or item may be lost until tasks are completed or you may impose longer lengths of time, depending on the situation. This works as long as you follow through with these efforts and are consistent.
Kids seem to be very cunning in their abilities to manipulate us, if we are not careful. I caution you not to treat your kids as the center of your universe by dropping everything because they will learn to expect this from others and the world does not work this way. It may also negatively reinforce the behavior by making her think that every time she wants attention, all she has to do is throw a fit and can become a habit.
I admit that using the techiniques I outlined concerned me because I did not want her to feel rejected and did not want to cut into what little quality time I had with her. However, it never seemed to hurt her feelings (it helps her cry less in the long-run) and improved the quality of our time spent together by not creating a situation where I had to appease her all the time or put up with the whining after a long day of work.