How to select a UV island? How do you select an entire UV island on a mesh by selecting a piece of the desired island?  Similar to the Ctrl+L for selecting all connecting geometry, only selecting all geometry within seams.

I.E. select a vertex within an island.



And hit some hot-key to extend the selection to the marked seams.



I use this feature all the time in 3ds Max, so I can unwrap a piece at a time. It would be a huge timesaver to be able to do this in Blender as well.
Update, UV islands in Vert/Edge/Face modes has been added

In the operator options, enable UV as a delimiter to select UV islands:


Select a vertex/edge/face.
Press Ctrl+LKey.
Enable UV option in toolbar.


Previous answer (Versions 2.74 or older)

Select linked can delimit by seams, but this only works in face-select mode *:


Switch to face select mode
Press LKey over the region, the selection will be restricted to the seams.


If you don't have seams around the UV island, you can automatically create them.


Image Window, UV -> Seams from Islands


* - this is intentional, select-linked traverses only faces in face-select mode, and edges in vert/edge mode.