It all depends really. YouTube and Google are good examples of where Flash Server accels since one of the features of Flash Server is the support of Streaming Video. The Flash Server product sheet can be found here:
http://www.adobe.com/products/flashmediaserver/
But really what you need to ask yourself is: are you going to be delivering alot of streaming media, video bloging, need support for direct AV ins, etc. If you don't then you could get away with just purchashing Flash and developing your movies and deploying them to the web. (Even without flash server you could still play movies through a flash interface, flash server is just more optimized to handle that task)
The only thing you will need on your network would be that all internet browsers have the flash plugin.
hth.
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