From my experience, nothing unusual happens to the guitar whether you leave it tuned to standard or drop tuned. Over the years, the neck wood will yield to the stresses and might bend a very tiny bit. To correct this, your guitar has a truss rod which when tightened straightens the neck back to original level. This is why you should get your guitar set-up once in a while.
As far as leaving it a stand or case or whatever, besides the obvious possibility of damage due to dropping the instrument I don't see any advantage of one over the other. If anything, it would be better to leave it in a case to avoid too much of temperature and humidity related issues. When the humidity in the air around the guitar increases, unfinished parts of wood absorbs moisture and expands. Similarly, heating expands solids in general. So when different joints (neck and fingerboard / wood and paint) get heated, differential expansion causes bending/cracking (like a bi-metallic strip).
So if you really are concerned about your valuable guitar, leave your guitar in a case in a cool place. Also, use a wax polish and fretboard oil to keep moisture out.
For acoustic guitar you can get a hydrometer to monitor and a humidifier to regulate humidity. The necessity of all this obviously depends on the value of your guitar...
-- My current rig
Guitar: '98 MIJ Ibanez RG520 QS w EMG 81/60
Amp: Laney LC15R Tube, Fernandes 20W SS
Pedals: MI Audio Tube Zone Overdrive, Boss OD3, CS3, MT2, HM2, DS2, CE5, DD7, TU3, Beta Aivin DD2 Delay, Dunlop Crybaby 95Q, Stranger Vol Pedal, BBE SupaCharger
Others: Yamaha RBX 374 Bass, Yamaha MM-6 Synth, M-Audio Fast Track, Shure SM-57, Heet Sound E-Bow Plus
Wanted(pm if selling): EB VPJr/Boss FV500L,Ibanez w Original/Lo-Pro Edge