This answer has been copied, pasted, and updated based on a related question that I answered.
I will answer your question related to hanging your guitars on the wall after I give some basic context on how to properly store a guitar in general. I think it's worthwhile to provide some context in which to answer your question. In essence, when it comes to guitars, you want to control a couple of main factors: temperature, humidity (relative), light, and outside damage. This applies to both "artwork" guitars and your average everyday player. How rigorous you are with this will affect the outcome of how well kept your guitar is.
Temperature & Humidity
A guitar is an organic instrument. It is made from wood, and wood has some interesting properties. First off, it's hygroscopic; this means it absorbs water. That makes sense based on what we know about trees :D. A guitar, despite the fact that most are sealed by either a polyurethane or a nitrocellulose finish, will absorb water from its surroundings and consequently move around a bit. Luckily, most designers and luthiers already know this--so it's highly unlikely that your instrument will warp to an unusable state just because you don't have a perfectly controlled environment. However it is recommended that you attempt to avoid extreme changes in environment--which includes both temperature and relative humidity--as these kinds of radical shifts can damage finishes of all types, cause bindings to pop loose, and all kinds of other nasties.
Typically both acoustic and electric guitars like to live at anywhere from 30% to 50% relative humidity--which is good, because we humans like that range too (at least I do). Any wetter than 50% and things start to mold, and any drier than 30% and you could potentially see the finish checking or even cracking in extreme cases. Grab yourself a hygrometer, many places sell them, and at minimum be aware of the room parameters where you keep your nice guitar. No real need to be paranoid about it. I have a 1930's Kay (not worth much, but old as the hills and sounds divine with a slide) and I keep it in the same room I keep my R8, Telecaster, and Firebird.
As with any fine piece of artwork, the constant abuse of photons on a surface can cause some wear and tear over many, many years. You can search the internet for pictures of 50's Les Pauls that used to be tobacco burst, but are now very much approaching an iced tea burst. Years of direct light can cause finishes to fade and check. Although this is highly unlikely to be a problem in most cases, if you plan on keeping a guitar for many years then place it in its case when you aren't using it and do your best to keep it out of direct sunlight.
This is the likely reason any guitar would be damaged. Kids playing, cats being curious, or dogs being rowdy--your guitar will get a ding. The only way you can prevent this is to lock it away in a safe, or a sealed glass case. The only advice I have here is don't be super paranoid about it, and make sure to place the guitar in its case when the relatives come over. If you are truly using an expensive guitar as a piece of art--something along the lines of the PRS private stock line--and never have plans on playing it, I would recommend a glass display case. This would reduce outside sources of damage but allow you, your family, and everyone else to enjoy the beauty of the piece. If you are simply worried about your 1958 reissue getting a ding then I think a glass case or safe is likely overkill; the guitar's case will protect it adequately. Safes are useful to store very valuable guitars for future generations to enjoy, but for anything outside an original 1950's Les Paul, Stratocaster, or Telecaster/Nocaster it's not really worth the investment in my opinion. Additionally I think that you should enjoy it anyway--we all eventually take a dirt nap. If you spent a ton of money or time procuring or building "your" special guitar then you should enjoy it before you pass it on to the next lucky owner.
Should I hang my guitars on the wall?
Well, you can--but do so with caution. Some finishes dislike the cushioning that wall mounts use and it can cause some issues. Additionally, there's a chance that your guitar might be knocked off the wall--which certainly would cause more damage than storing it in its case or keeping it on a stand. I wouldn't recommend hanging very expensive guitars without researching some sturdy, finish friendly mounts, of which I have found none. Some stands can also damage the finish of your guitar when left in contact for long periods of time, but placing an old used T-Shirt over the cushions can fix that issue (this also works on wall hangers if you go that route). In general I would recommend placing an unused guitar safely in its case or on a protected stand if you plan to play it frequently. I think that a well placed guitar can improve the aesthetics of a room quite nicely--or maybe I'm just lucky because my wife doesn't seem to mind at all :).