For years, BitTorrent has been a popular way to download and share files. On Linux, Azureus has always been the dominant client for connecting to the network, and for a while, people were satisfied. But, as the network grew, more people were not happy with Azureus, even though it has a plethora of features. There were several flaws in it, and while minor, other torrent clients began to spawn.
Deluge supports encryption, UPnP, DHT, and other features that have become standard in most BitTorrent clients. It even supports µTorrent's Peer Exchange functionality.
However, the best features of Deluge are not in the main interface, but rather included in the plugins that come with it. For example, the Scheduler plugin lets you define time slots when bandwidth should be unlimited, throttled, or just halted.
Other plugins let you define a target share ratio, create torrents, and even run searches on popular torrent trackers.
The development of Deluge has been going at a very fast pace, with useful new features added each release, which usually is every few months. The latest version (featured in the screenshots) is 0.5.2. You can download it at deluge-torrent.org.
Happy torrenting, and, er.. stay legal!