Can you recommend some framework/tool for widgets?

On my site I have a dashboard and I want to put there different information in blocks. For example, messages, chat, current status, most common actions, etc. So I will not mistake, if call such block widget right?
According to user preferences and screen resolution, I need such blocks be resizable, add/remove, movable, fit to screen width and (important) with settings saving - i.e. after user did adjustment and log-out/logined or refresh page, they should be on same places.

I searched the web and found nothing. If you know or have some idea, please, give me a hint.

Additional information:
I am using JQuery on site. Ideal solution should be under free licence.