Maybe I'm doing something wrong, but when I cancel a long-running query it seems to continue to block the active connection, meaning I can't run another query. I can't even close SQL Developer because of the "Connection is currently busy. Try again?" dialog.
So is there a problem with cancelling tasks? And is it possible to add "Force quit" to the current options of "Try again" and "Abort"?
The behavior depends on your SQL Developer version and the Oracle database client software you have installed. Are you using the latest version of the tool, 3.2.20.09.87? Do you have Oracle database client software installed?
I recall that with some prior SQL Developer releases, we could mistakenly pickup ojdbc5 rather than ojdbc6 from the Oracle client, but with no client installed we default to the ojdbc6 version that ships with the tool. That version has improved support for query cancellation. If you want a more detailed history (or additional workarounds you might want to try), read through the following: How to cancel long query?
By default, SQL Developer uses a single connection for the object browser and the worksheet (and any additional worksheets you open for that connection). You can create a worksheet with its own connection using ctrl-shift-N when the work sheet has the focus.
You can cancel a query in a worksheet (subject to the possible limitations Gary mentions), but there is no way to cancel a long running query in an open object AFAIK.
This doesn't solve the problem of wanting to use the object browser when the primary worksheet or an open object is using the connection. I have thought of requesting the option to create a new browser with a separate connection, but I think multiple object browsers, and keeping track of which open worksheets and objects belong to which browser, could be very confusing.