I only really turn the forum offline if I need to update the forum software. In most other cases there really isn't a call for it. Even if I'm shuffling sections of the forum around I don't bother turning things offline.
I never normally find much of a use for it unless I am doing a big upgrade to the software or something like that - everything else I do on a test forum then pull over whilst the other forum is still live.
I only use this feature when I am making big updates to the forum. However I try to avoid using this when possible because members won't be able to access the forum when this happens.
Indeed I do; usually for routine maintenance, site changes, plugin updates, and even theme updates. It's good to take everyone offline for a bit, and if you don't you would need to go through .htaccess to get everyone off and that's just a pain in the caboose.
I've only used it for bigger changes, like upgrades, moving host and such things. That's basically the only time I see a need to have the forums disabled.