Many users install Azureus to get a full-featured bittorrent client, but it is slow and uses a large amount of memory. uTorrent isn't available on Linux, but a nice little Gnome-friendly app called Deluge is!
It can easily handle ten or more torrents without affecting your CPU or memory in a significant way. The Deluge site says
When Deluge was first released in September 2006, it was very limited and lacking in features, but over the last year, Deluge has been one of, if not the most rapidly developed bittorrent client on the web. Now, Deluge is among the most feature-rich clients in development (second only to Azureus, but without the bloat, and ahead of µTorrent according to http://en.wikipedia.org/wiki/BitTorrent_client) , and it does this without the need of tools such as Java or Wine. Deluge was created with the intention of being lightweight and unobtrusive. It is our belief that downloading shouldn’t be the primary task on your computer, and therefore shouldn’t monopolize system resources.Plugins
Deluge offers a large number of plugins, too, extending the funtionality of Deluge.
Network Health Monitor
Linkage is another client that works well within Ubuntu, but it's still quite new and lacks the features (especially the plugins) that Deluge has.
Good luck torrenting!!!