If it's in a case it's less likely to get damaged from other things.
But it doesn't really matter.
There's a good chance that what I've written above is useless and if you take any of the advice it's your own fault.
Depends. Do you have clumsy people/children/pets in your home that could come along and do damage to your guitar? If not then by all means leave it on a stand. Otherwise I would put it in a case to keep it safe.
it's safer in a case. if you put it on a stand it could get knocked over, and if it's a gibson, or something with a similar headstock design to gibson, that usually means broken headstock.
Live Rig January 2018

Fender Baja Telecaster/Danelectro DC-12
Boss TU-3, Ibanez TS-9, Fulltone OCD 1.7, EHX Small Clone, MXR Carbon Copy, EHX Holy Grail Neo
1964 Vox AC30TB with '69 Rola G12M "blackbacks"
Elixir Nanoweb 10-52 strings, Dunlop Jazz III XL picks
Lean it against your amp just kiddin' I usually put the guitar or bass back in it's gig bag (mind you it's not really a case) if I think I'm not going to play or I know I shouldn't play (i.e. my parents just told me to shut it down) or I just randomly put it on a stand or lean the top of it's headstock on a bookcase or something (I've learnt not to lean them with the contact point being on the neck). Up to you, if you're at home it shouldn't get damaged anyway.
Quote by Tyson2011
when in doubt, adjust the truss rod.

Sfedf the First ...
or should it be the insane?
I recommend putting it in the case, just as a precaution - unless the room is perfectly safe (pets, children, wind, idiots) or you find it terribly annoying having to get it in/out each time.
call me ziggy.
i keep them all in the cases when not in use.. i rather be safe then sorry. yes it takes a few more secs to get it out of the case but rather those few secs extra then have it be busted....
I keep mine on a stand, I'm the only one who ever comes into my room, and I'm usually not that clumsy, plus my stand is usually pretty stable. I might put them in their cases though if I know I'm going to be coming home drunk.
you could get a wall hanger that locks the guitar in place? I have mine in it's case at the moment, but just because I haven't gotten around to putting up a hanger (just moved house). If its hanging on your wall it should be pretty safe if you get a secure hanger, plus it gives you more room on your floor, and looks pretty hanging on your wall