While I agree that there are no real risks to string your wheels by the rim, there are a number of DIY and commercial wall mounted racks for hanging wheels at the axle.
Wheelzrack makes one good option, and even integrates a storage shelf for shoes and helmets.
They support up to for sets of wheels, which may be a good option in your case.
Feedback sports used to offer a Wheel Arm system, which had a bolt-to-wall mounting option (note: the Wheel Arm is no longer listed on home page
but they sell alternate models).
These are designd for shop displays, but will work in the home as well, assuming your significant other is tolerant. :-)
Hope that is helpful.
bicycles.stackexchange.com/users/1259/zenbike
As suggested by this answer , there's really no problem with hanging wheels or even an entire bike up by the rims.
It's a good idea to pad the hook to avoid scratches, but this should be easy enough with some cheap foam or even tape.
Failing that, a narrow shelf with some blocks either side of each wheel to stop them rolling away would work and take up little space.
I imagine you could even use a short loop of rope to hold a couple of wheels.
To avoid touching the rims, you could loop this between the spokes and around the hub.
If the wall is rough, cover it with some cardboard or thin foam/rubber.
bicycles.stackexchange.com/users/5337/James Bradbury
If they are QR hubs you could remove the skewer and pass a length of cord through the axle, then knot it, so that the wheel could be hung by the cord.
bicycles.stackexchange.com/users/1584/Daniel R Hicks
I have an old steel coffee-table leg screwed to the wall of my carport by the flanges at the top of the leg.
It holds about 6 random rims normally, and sticks out slightly upwards To get more space and protect the nicer aluminium ones, I use a length of ribbon or soft rope like sash cord.
This goes around the rim and is tied in a loop with ~100 mm of slack.
Then the loop is hooked over the leg and left to hang.
Works well for me.
Advantage - soft cloth is in contact with the rim.
Downside -
its still hanging by the rim.
Another option might be a frame somewhat more like a dishrack but for storing wheels?
Advantage - rims are protected Downside - you'll have to make it.
And it will chew up floor space unless you make a wall-mounted one.
Final thought -
how about one of these cheap wheel stands for each one?
Advantage - Just buy them, no making required Downside - Floor space used up/clutter Plus
even cheap ones are $11-$12 US each which adds up.
bicycles.stackexchange.com/users/19705/Criggie
Put them in wheel bags and simply hang the bags up.
Keeps wheels protected, clean and dust free.
That's what I do.
bicycles.stackexchange.com/users/13358/alexsimmons
Another option, very simple DYI is to make a pair of clamps for each wheel, eg.
metal plates (spacers?) , big enough to drill two holes: one to put axle through and one to pass cord through.
Hang that cord on the hook or wherever you like.
bicycles.stackexchange.com/users/25953/krzyski
You either need to use the axle or support from below if you are not wanting to hang from the rim.
If you're going to slide them on a skewer then the other answers have plenty of suggestions.
If you're supporting from below, assuming you are leaning them against the wall
then you need either a shelf or 2 poles perpendicular the the wall.
You could hold poles up with shelf brackets and since your wheels will be light anyway you could get several deep.
You could anchor the end of the poles to the ceiling too if need be.
bicycles.stackexchange.com/users/26481/Chris
HANG THEM BY
THE RIMSeriously get some hooks with a rubber coating on the outside from something like home depot or lowes or Amazon.
then hang up the wheels.
YOU WILL NOT SCRATCH THE RIMS.
I hang my zipp 808 like this and they are fine.
Heck, they are fine even when they have a bike attached.
Look man I get beeing protective about the wheelset you just dropped hundreds of dollars on but you will waste more of your precious money or time if you don't go this route.
Thats my 2 cents.
Best of luck to you
bicycles.stackexchange.com/users/23778/KidCoder
I have 5 pair of extra wheels, which I would like to store on the wall efficiently.  I am a little skittish about storing them using the rim since some of them are carbon wheels and I don't want to risk scratches. Any suggestions?
How can I store my extra wheels on the wall efficiently, without hanging them by the rim?
bicycles.stackexchange.com
<wheels><storage>
bicycles.stackexchange.com/questions/30161
bicycles.stackexchange.com/users/19188/Nyotom
There are no real risks to string your wheels by the rim, there are a number of DIY and commercial wall mounted racks for hanging wheels at the axle. Wheelzrack  makes one good option, and even integrates a storage shelf for shoes and helmets. Feedback sports used to offer a  Wheel Arm  system, which had a  bolt-to-wall mounting option. Another option might be a frame somewhat more like a dishrack but for storing wheels. You either need to use the axle or support from below if you are not wanting to hang from the rim.  Other alternatives included a short loop of rope or using wheel bags. There should be no risk from hanging wheels or an entire bike from suitably padded hooks, although there are commercially available racks that hold wheels from the axle or base. These can also be built yourself. Wheels could also be suspended with rope rather than hooks, or placed in wheel bags that are hung from hooks.
There should be no risk from hanging wheels or an entire bike from suitably padded hooks, although there are commercially available racks that hold wheels from the axle or base. These can also be built yourself. Wheels could also be suspended with rope rather than hooks, or placed in wheel bags that are hung from hooks.