For Downloading I have to recommend Download Accelerator Plus or Pro. Even GoZilla! is good but Download Accelerator Plus is faster and less resource hungry.
For FTP the two best FTP clients I know are:
Cute FTP and WS FTP.
I prefer Cute FTP as it is much much much more user friendly.
You can also use a People to People sharing software like Napster except with it you can exchange files legally. The best softwares to use are:
MusicCity Morpheus or
KaZaA Media Desktop.
With People to People sharing it is faster as the software searches for a person having the file in a nearby locality giving least amount of server lag.
Now P2P sharing is really hot.