First is to make sure that you have setup your ports in Vuze properly especially if you are behind a firewall or router. You'll need to add an exception for Azureus.exe (the main Azureus process) to your Software firewall (Windows)].  If you are using a Mac, check your firewall settings under (System  Preferences > Network).  And it is necessary to forward Azureus' TCP and UDP listening port (see Tools -> Options -> Connection) from your router to your PC, there are 2 ways to do that:

   - When your Router supports UPnP  you may want to enable it in the router configuration and in Vuze (Tools > Option > Plugins > UPnP)
   - If UPnP isn't supported or doesn't work correctly you have to do manual Port forwarding.

Downloading as fast as your connection allows requires good settings based on the upload speed of your Internet connection. First, fix your NAT problem if you never see and do not Force Start your torrents. Running another P2P program while Vuze is running will stall your downloads badly.

NOTE:  Make sure to check out: Bad Routers and Bad ISP's