Add the ability to click and drag tabs (Queries, channels, networks, etc) out of Konversation's main window, thus spawning a new window to contain them. The behavior should be basically identical to how Google Chrome works.

This one feature would satisfy many other potential requests. I've mainly seen them in Konversation's IRC channel so I can't make any references to bug reports, though.

Some of the features this would satisfy are as follows:
"Dual chat pane" (Chat pane gets split in half and shows streams from two channels at once)
"Collapsible networks" (Clicking Freenode's tab/list entry causes all channels and query tabs associated with it to disappear until clicked again)
"Channel merging" (Treat two channels on two networks that share the same name as one channel -- This would work better using detachable tabs since you could drag both channels to the same window and still see them as separate channels, yet a highlight would make the same taskbar entry flash.)
"Multi-row tabs/Make the channel pane fit more stuff" (Both these requests deal with trying to fit more channels, networks and queries into the same space without having to use a scroll bar. If more windows could be made, this problem wouldn't occur as much.)

In addition to all this, it could completely change the look of Konversation if used correctly. Each channel and query could appear in their own tab by default, giving it the feeling of being an IM client rather than an IRC client. This should be configurable if implemented so that users may decide to automatically "dock" every new tab to the network that owns it (IRC-like) or creates a new window when a new tab is opened (IM-like).

This should ultimately be a functional change, not an aesthetic one, just to be clear. Any aesthetics that do come up are done by how the end user arranges the tabs, not by any changes in Konversation's GUI.