KTorrent

Maybe used as an inpiration for uTorrent's interface (the most popular BitTorrent software for windows), KTorrent is built using the KDE library and hence is a KDE application.

Written in C++ using the Qt user interface toolkit, ktorrent is maintained in the KDE Extragear.

KTorrent supports UDP trackers, has an IP address blocklist plugin, Port forwarding with UPnP, Protocol encryption, file prioritizing and can import partially downloaded files.
KHTML enables internet searching with torrent search engines.

Manual addition of trackers, download/upload speed throttling and scheduling are also possible with KTorrent.
One can create a torrent using KTorrent but to seed you need a torrent tracker.

Newer versions support IP v6 and SOCKS v4 and v5 and have a new queue manager UI.

It also allows to remove individual files from a torrent and also supports RSS feeds. A number of plugins are available to enhance features.

Being a KDE application KTorrent is most popular amongst KDE users.

Deluge

Deluge is another BitTorrent client created using Python and GTK+ and uses the libtorrent C++ library.
The software works in any POSIX compliant OS.

Originally built to bring a native, full-featured client to GTK desktop environments such as GNOME and Xfce, official Windows and Mac OS X compatible versions are also available.

Deluge is extremely user friendly and can download multiple files in a single window, select files from a torrent before beginning the download, specify global download directory, and a completed download directory and stop uploading a torrent once it has reached a specified ratio.

Deluge enables prioritizing the first and last parts of the file to enable preview of media files in addition to many of the basic but important features like BitTorrent Protocol Encryption, UPnP and NAT-PMP.

Plug-ins are available to enhance performance: Blocklist Importer, Torrent Creator, Torrent Search.

Though Deluge is superior in various features its UI is slower. Also its pre-compiled package is very large compared to other clients.

Transmission

Transmission is the official BitTorrent client for Ubuntu due to its minimum resource usage and usability.
It aims at providing a simple and spontaneous user interface on all platforms.

Written completely in C++ the whole package is just 330 KB.

There is also a Transmission client available for Mac OS X and one available for Android by the name of Transdroid.

It has almost all the features as the previous clients like having the ability to customize downloads to individual files in the file selection menus, IP v6 support, HTTPS tracker support, automatic port mapping with UPnP, torrent file creation and Encrypted peer connections.

Installation

You can find them in your distribution package manager ready to be installed and used.