Stuck task in management studio, how do you handle them?

I would say don't ever use the "Take Offline" thing in the GUI unless you know for a fact that the database is not in use. By anything. That's hard to know without doing some legwork, so why not save this script somewhere and always use this?

USE [master];
GO
ALTER DATABASE $dbname$ SET SINGLE_USER WITH ROLLBACK IMMEDIATE;
GO
ALTER DATABASE $dbname$ SET OFFLINE;

And then the reciprocal of course:

ALTER DATABASE $dbname$ SET ONLINE;
GO
ALTER DATABASE $dbname$ SET MULTI_USER;

The reason you need to set it to SINGLE_USER first is to kick out any existing users (there is an option to do so on the detach dialog, but not the take offline dialog), since SQL Server needs exclusive access to the database in order to take it offline. Now, you may want to do some extra legwork anyway to see who is currently using the database, as if you do this in the middle of a large backup operation or ETL job or what have you, that might be problematic.

EDIT : I have filed a suggestion on Connect about this (see Connect #2687832) and have also posted it to Trello (filed under "Object Explorer").

This was fixed in SSMS 16.3; there is now a checkbox that asks if you want to forcefully terminate any active connections.

When you're already in the hanging situation, don't forget you can search open connections across the server with

sp_who2  

in another database, such as master.
Scan the results for any where the database is the one you are trying to take offline.
Note the spid (process id) column value of those rows.

One at a time, run

kill  ##

where "##" is the spid.

Certainly take care to make sure those processes aren't important to leave running... they will be terminated without even finishing the latest command and without warning.