I think it would be a cool idea to be able to install software from the software center or apt-get or even synaptic, to a thumb drive, external hard drive, or a SD Card.

Not only to install to any portable storage but to also take that storage image of installed applications to desktop, laptop, tablet, cellphone, and run it like it is a local application.

This way if you are working with projects or have saved games, you can have that progression from one device to another without the need for installation of application on whatever device you are plugged into.

Also it would be nice if this application image could have public or private server/could sync capabilities.