Azureus implements the BitTorrent protocol using java language and comes bundled with many invaluable features for both beginners and advanced users:

Multiple torrent downloads
Upload and download speed limiting, both globally and per torrent
Advanced seeding rules
Adjustable disk cache
Only uses one port for all the torrents
UPnP sets the forward on your router
Can use a proxy, for both tracker and peer communications
Fast resume
Can set a default download dir and move completed files
Can import torrents automatically from a set dir
Highly customizable interface
IRC plugin included for quick help
Embedded tracker, host your own torrents, automate your shares (periodic scanning of a dir)...
Distributed Hash Table: host on it a completely decentralised torrent and/or benefit from it when the tracker is offline.

Many useful plugins are available:

Auto-adjustment of your upload and download speeds according to your network charge with Autospeed
Auto-download torrents with RSS Feed Scanner
Schedule upload and download speed limits with Speed Scheduler
Receive a mail when a download finishes with Status Mailer
Add numerous info on torrents (Extra seeding columns, Country Locator)
Remote control Azureus through the Swing Web Interface or the HTML Web Interface