I'd like a small javascript scratchpad in which I can write and test (non-DOM related) functions.
I'm not happy using the Firebug console to do this.
Does such a thing exist as a standalone app?
There's jQueryBuddy, currently in beta.
It does support DOM manipulation, but you don't have to use that if you don't need it. And like LinqPad it has a very similar Dump() method for viewing objects.