I'm working on a patch/plugin adding support for creating parallel ways to JOSM.
The current form is a patch to the core, but depending on how people feel about including it in there and how fast the quality improves, I might change to a plugin.
Feedback and testing is welcome. (preferably in the trac ticket)
Use Shift-P or the button (same icon as in potlach2) to activate the mode. You may ctrl/shift select ways as in select mode. To create a parallel path just drag one of the selected ways. (or just a single way).
See usage description in the statusline for more.
Probably best to not use it for uploads yet. I'm not that familiar with the code-base and strange bugs might lurk around.
(Edit: added short usage description)
UPDATE: now a plugin: http://wiki.openstreetmap.org/wiki/JOSM/Plugins/ParallelWay