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

Features:

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